dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/03/01   6:38 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         1.94236
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const           -6.2979        1.3167   -4.783   0.0000      0.0000
TASK             0.1063        0.0613    1.733   0.0415      0.0000
RIGHTS           0.1534        0.1328    1.155   0.1241      0.0000
ELITE            4.7187        1.2474    3.783   0.0001      0.0000
SAL             -0.1808        0.1786   -1.012   0.1557      0.0000
COL              0.1377        0.0771    1.786   0.0370      0.0000
WI               3.4064        1.1406    2.987   0.0014      0.0000
LA               1.1227        1.1842    0.948   0.1715      0.0000
DE              -1.1192        1.1280   -0.992   0.1606      0.0000
RI              -2.8039        1.2136   -2.310   0.0104      0.0000
const            0.4704        0.2327    2.022   0.0216      0.0000

Correlation matrix of the parameters
   1.000   0.341  -0.036  -0.498   0.211  -0.818  -0.188  -0.168   0.070
   0.122  -0.421
   0.341   1.000  -0.108  -0.287   0.031  -0.460   0.122  -0.028   0.068
   0.042   0.310
  -0.036  -0.108   1.000  -0.148  -0.356   0.026  -0.154   0.084  -0.046
  -0.116   0.165
  -0.498  -0.287  -0.148   1.000   0.223   0.000   0.109   0.130  -0.053
  -0.339   0.315
   0.211   0.031  -0.356   0.223   1.000  -0.394   0.016   0.029  -0.060
  -0.074  -0.106
  -0.818  -0.460   0.026   0.000  -0.394   1.000   0.089   0.069  -0.062
   0.077   0.101
  -0.188   0.122  -0.154   0.109   0.016   0.089   1.000   0.036   0.007
  -0.010   0.261
  -0.168  -0.028   0.084   0.130   0.029   0.069   0.036   1.000  -0.003
  -0.044   0.093
   0.070   0.068  -0.046  -0.053  -0.060  -0.062   0.007  -0.003   1.000
   0.048  -0.074
   0.122   0.042  -0.116  -0.339  -0.074   0.077  -0.010  -0.044   0.048
   1.000  -0.212
  -0.421   0.310   0.165   0.315  -0.106   0.101   0.261   0.093  -0.074
  -0.212   1.000

Number of iterations    3
Minutes to convergence     0.00511

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
      0.22160397       0.60300336 
      0.10101431       0.13774525 
      0.34934053       0.63036831 
    -0.085065340      -0.18463570 
      0.17802201       0.37540668 
      0.20932212       0.61994947 
     0.069752993       0.27138807 
    -0.069538178      -0.19219607 
     -0.17298920      -0.30898262 
alpha= 0.52286 
beta= 1.07769 
ave mean= 0.32667 
ave var= 0.08458 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.360      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.944      Std error of est:                 0.220
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.963429    0.229859   -4.191381     0.000       ---         ---  
X1           0.014216    0.009444    1.505231     0.140    0.189569    0.606581
X2           0.020866    0.027041    0.771619     0.445    0.086966    0.441778
X3           0.966330    0.239631    4.032584     0.000    0.467892    0.621866
X4          -0.044700    0.036695   -1.218141     0.230   -0.132979    0.008212
X5           0.034253    0.014661    2.336321     0.025    0.281867    0.453771
X6           0.821737    0.228384    3.598056     0.001    0.322567    0.313797
X7           0.166559    0.226446    0.735535     0.466    0.065381   -0.035959
X8          -0.215741    0.224952   -0.959052     0.343   -0.084688   -0.082752
X9          -0.530547    0.238320   -2.226191     0.032   -0.208262   -0.082752

 0.13659 
 0.06266 
 0.33713 
-0.09582 
 0.20310 
 0.23242 
 0.04711 
-0.06102 
-0.15006 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  161.930      Degrees of freedom:                  40
R-squared:                   0.811      Rbar-squared:                     0.768
Residual SS:                30.602      Std error of est:                 0.875
F(9,40):                    19.073      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.302264    3.399147   -4.501796     0.000       ---         ---  
X1           0.598213    0.268301    2.229634     0.031    0.253457    0.702647
X2           0.292582    0.107794    2.714263     0.010    0.241672    0.550418
X3           2.641677    0.496372    5.321974     0.000    0.468803    0.651090
X4          -0.502262    0.334016   -1.503707     0.141   -0.123646    0.077521
X5           1.893316    0.984129    1.923850     0.062    0.195191    0.456340
X6           2.710133    0.901357    3.006727     0.005    0.210834    0.245829
X7           2.330401    0.903376    2.579659     0.014    0.181293    0.081851
X8          -1.812607    0.897693   -2.019184     0.050   -0.141011   -0.120529
X9          -3.361353    0.920328   -3.652341     0.001   -0.261495   -0.120529

 0.04313 
 0.04100 
 0.08669 
-0.02049 
 0.03275 
 0.03549 
 0.03033 
-0.02342 
-0.04460 
-0.00654  1.42031 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00990  0.99990 
 0.06078  0.95937 
-0.18060  0.99990 
-0.00654  1.42031 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.26000 
 0.02000 
 0.16000 
Beta is better if rb/ro<1 1.37832 
Beta is better if rb/rl<1 0.91032 
dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/14/01  11:35 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         2.50285
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const           -8.0296        1.0014   -8.018   0.0000      0.0000
TASK             0.1869        0.0530    3.527   0.0002      0.0000
RIGHTS           0.2864        0.0961    2.979   0.0014      0.0000
ELITE            7.7359        0.9030    8.567   0.0000      0.0000
SAL             -0.0650        0.0988   -0.658   0.2552      0.0000
COL              0.0123        0.0593    0.207   0.4181      0.0000
WI               6.1941        1.0443    5.931   0.0000      0.0000
LA               2.1619        0.3940    5.487   0.0000      0.0000
DE              -0.9885        0.9770   -1.012   0.1558      0.0000
RI              -1.3170        1.4712   -0.895   0.1853      0.0000
const            9.7627        0.8124   12.017   0.0000      0.0000
ELITE          -13.1175        1.3304   -9.860   0.0000      0.0000

Correlation matrix of the parameters
   1.000   0.462  -0.052  -0.565   0.493  -0.909  -0.060  -0.288   0.092
   0.077  -0.148   0.107
   0.462   1.000   0.143  -0.459   0.178  -0.564   0.053   0.023   0.035
   0.011  -0.174   0.271
  -0.052   0.143   1.000  -0.105  -0.257  -0.057  -0.102   0.291  -0.055
  -0.105  -0.132   0.207
  -0.565  -0.459  -0.105   1.000  -0.044   0.284  -0.069   0.082  -0.108
  -0.231  -0.066   0.054
   0.493   0.178  -0.257  -0.044   1.000  -0.573  -0.021  -0.080   0.006
  -0.015  -0.181   0.149
  -0.909  -0.564  -0.057   0.284  -0.573   1.000   0.069   0.178  -0.059
   0.019   0.200  -0.195
  -0.060   0.053  -0.102  -0.069  -0.021   0.069   1.000   0.045   0.008
   0.049   0.161  -0.117
  -0.288   0.023   0.291   0.082  -0.080   0.178   0.045   1.000  -0.018
  -0.024   0.063  -0.006
   0.092   0.035  -0.055  -0.108   0.006  -0.059   0.008  -0.018   1.000
   0.045   0.018  -0.044
   0.077   0.011  -0.105  -0.231  -0.015   0.019   0.049  -0.024   0.045
   1.000   0.149  -0.164
  -0.148  -0.174  -0.132  -0.066  -0.181   0.200   0.161   0.063   0.018
   0.149   1.000  -0.966
   0.107   0.271   0.207   0.054   0.149  -0.195  -0.117  -0.006  -0.044
  -0.164  -0.966   1.000

Number of iterations    10
Minutes to convergence     0.02071

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
      0.20480700       0.83569118 
     0.095118030       0.14178999 
      0.31966314       0.67685933 
    -0.015259302     -0.035169970 
    0.0079663891      0.017028033 
      0.19943395       0.87191171 
     0.067296232       0.42291004 
    -0.030641693     -0.075819281 
    -0.040860618     -0.090189623 

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
     0.012511709     0.0040079486 
    0.0062311314     0.0086862789 
      0.11217608       0.19551443 
   -0.0010196330    -0.0024300097 
   0.00053252332     0.0011351904 
     0.012237847    -0.0074869469 
    0.0044532253      0.012676397 
   -0.0020441991    -0.0055521059 
   -0.0027214105    -0.0067082222 
alpha= 1.27815 
beta= 8.93595 
ave mean= 0.12514 
ave var= 0.00976 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.360      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.944      Std error of est:                 0.220
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.963429    0.229859   -4.191381     0.000       ---         ---  
X1           0.014216    0.009444    1.505231     0.140    0.189569    0.606581
X2           0.020866    0.027041    0.771619     0.445    0.086966    0.441778
X3           0.966330    0.239631    4.032584     0.000    0.467892    0.621866
X4          -0.044700    0.036695   -1.218141     0.230   -0.132979    0.008212
X5           0.034253    0.014661    2.336321     0.025    0.281867    0.453771
X6           0.821737    0.228384    3.598056     0.001    0.322567    0.313797
X7           0.166559    0.226446    0.735535     0.466    0.065381   -0.035959
X8          -0.215741    0.224952   -0.959052     0.343   -0.084688   -0.082752
X9          -0.530547    0.238320   -2.226191     0.032   -0.208262   -0.082752

 0.13659 
 0.06266 
 0.33713 
-0.09582 
 0.20310 
 0.23242 
 0.04711 
-0.06102 
-0.15006 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                 1189.472      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:               363.629      Std error of est:                 3.015
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -18.265392    3.143519   -5.810491     0.000       ---         ---  
X1           0.136142    0.129159    1.054058     0.298    0.132749    0.579444
X2           0.327376    0.369815    0.885244     0.381    0.099773    0.444637
X3          14.288819    3.277147    4.360140     0.000    0.505900    0.626741
X4          -0.541297    0.501841   -1.078622     0.287   -0.117749    0.020036
X5           0.478761    0.200501    2.387827     0.022    0.288083    0.449070
X6          11.174020    3.123337    3.577590     0.001    0.320734    0.315471
X7           3.296071    3.096835    1.064335     0.294    0.094609   -0.010946
X8          -3.332471    3.076409   -1.083234     0.285   -0.095654   -0.089295
X9          -7.897951    3.259231   -2.423256     0.020   -0.226699   -0.089295

 0.18973 
 0.14212 
 0.70115 
-0.16802 
 0.41723 
 0.46431 
 0.13470 
-0.13620 
-0.32728 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  161.930      Degrees of freedom:                  40
R-squared:                   0.811      Rbar-squared:                     0.768
Residual SS:                30.602      Std error of est:                 0.875
F(9,40):                    19.073      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.302264    3.399147   -4.501796     0.000       ---         ---  
X1           0.598213    0.268301    2.229634     0.031    0.253457    0.702647
X2           0.292582    0.107794    2.714263     0.010    0.241672    0.550418
X3           2.641677    0.496372    5.321974     0.000    0.468803    0.651090
X4          -0.502262    0.334016   -1.503707     0.141   -0.123646    0.077521
X5           1.893316    0.984129    1.923850     0.062    0.195191    0.456340
X6           2.710133    0.901357    3.006727     0.005    0.210834    0.245829
X7           2.330401    0.903376    2.579659     0.014    0.181293    0.081851
X8          -1.812607    0.897693   -2.019184     0.050   -0.141011   -0.120529
X9          -3.361353    0.920328   -3.652341     0.001   -0.261495   -0.120529

 0.04313 
 0.04100 
 0.08669 
-0.02049 
 0.03275 
 0.03549 
 0.03033 
-0.02342 
-0.04460 
-0.00654  1.42031 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00990  0.99990 
 0.00474  0.98600 
-0.18060  0.99990 
 0.00080  0.99990 
-0.00654  1.42031 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.26000 
 0.00000 
 0.00000 
 0.02000 
 0.16000 
Beta is better if rb/ro<1 0.84202 
Beta is better than logit trans if rb/ro<1 0.60714 
Beta is better if rb/rl<1 0.55611 

 0.00990  0.01484 -0.06902  0.00074 
 0.06138  0.31139  0.31153  0.07718 
 0.00990  0.03367  0.11977  0.02434 
 0.16236  0.40517  0.39186  0.18638 
 0.00990  0.00670 -0.01270 -0.00429 
 0.00990  0.00947 -0.11593 -0.00423 
 0.00990  0.02802 -0.03210  0.00321 
 0.00990  0.01055 -0.18060 -0.00509 
 0.00990  0.02485  0.12422  0.01229 
 0.00990  0.04366  0.00990  0.00000 
 0.00990  0.00474 -0.10089 -0.00578 
 0.00990  0.06413  0.12399  0.02085 
 0.08712  0.04484  0.03688  0.01676 
 0.00990  0.04664 -0.00763  0.00052 
 0.99990  0.62196  0.69950  0.30364 
 0.00990  0.08447  0.14586  0.00856 
 0.00990  0.02444  0.02169  0.00393 
 0.00990  0.01202  0.01761  0.00195 
 0.02772  0.08904  0.28736  0.04974 
 0.00990  0.02941  0.12305  0.01807 
 0.00990  0.06857  0.10548  0.01466 
 0.00990  0.02352 -0.01001  0.00908 
 0.00990  0.18300  0.29933  0.08092 
 0.00990  0.04211 -0.01861  0.01371 
 0.00990  0.01738 -0.00459  0.00231 
 0.99990  0.61753  0.56746  0.39720 
 0.00990  0.03326  0.00477  0.00824 
 0.00990  0.03522  0.09773  0.01618 
 0.00990  0.01180 -0.13053 -0.00654 
 0.00990  0.01035 -0.15264 -0.00522 
 0.00990  0.03328 -0.06331  0.00010 
 0.12672  0.13176  0.12672  0.11682 
 0.00990  0.43322  0.00990  0.00000 
 0.10098  0.17918  0.21493  0.05389 
 0.03267  0.03036  0.03258  0.00854 
 0.46035  0.27872  0.34868  0.15336 
 0.03663  0.01697  0.04136  0.00522 
 0.04851  0.08187  0.13151  0.02726 
 0.11484  0.57254  0.56182  0.31611 
 0.17721  0.16369  0.30070  0.11225 
 0.15147  0.39175  0.36603  0.16655 
 0.99990  0.51346  0.40743  0.22251 
 0.18513  0.31051  0.27408  0.13191 
 0.35739  0.50971  0.61225  0.22459 
 0.99990  0.81558  0.60645  0.27203 
 0.43758  0.98525  0.83379  0.97515 
 0.99990  0.98600  0.99990  0.99000 
 0.99990  0.84813  0.73863  0.76481 
 0.99990  0.97347  0.91198  1.42031 
 0.99990  0.77361  0.71653  0.43334 
dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/14/01  11:37 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         2.61712
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const           -8.2138        0.9654   -8.508   0.0000      0.0000
TASK             0.1768        0.0480    3.686   0.0001      0.0000
RIGHTS           0.3778        0.1001    3.774   0.0001      0.0000
ELITE            7.0489        0.8929    7.894   0.0000      0.0000
SAL             -0.0911        0.0989   -0.921   0.1784      0.0000
COL              0.0342        0.0553    0.619   0.2679      0.0000
WI               5.7970        1.0705    5.415   0.0000      0.0000
LA               2.3361        0.2959    7.894   0.0000      0.0000
DE              -0.8921        0.9800   -0.910   0.1813      0.0000
RI              -1.0261        1.4761   -0.695   0.2435      0.0000
const            9.9657        0.7440   13.394   0.0000      0.0000
RIGHTS          -0.4755        0.1387   -3.428   0.0003      0.0000
ELITE          -11.8178        1.2171   -9.710   0.0000      0.0000

Correlation matrix of the parameters
   1.000   0.476  -0.004  -0.623   0.356  -0.908  -0.017  -0.362   0.091
   0.108   0.069   0.110  -0.138
   0.476   1.000   0.021  -0.395   0.133  -0.587   0.090  -0.041   0.035
   0.015  -0.144   0.227   0.159
  -0.004   0.021   1.000  -0.089  -0.287  -0.053  -0.194   0.251  -0.070
  -0.117  -0.094  -0.176   0.188
  -0.623  -0.395  -0.089   1.000  -0.064   0.324  -0.048   0.140  -0.112
  -0.245  -0.209   0.112   0.172
   0.356   0.133  -0.287  -0.064   1.000  -0.423   0.022  -0.049  -0.009
   0.015  -0.042   0.047  -0.001
  -0.908  -0.587  -0.053   0.324  -0.423   1.000   0.020   0.255  -0.057
  -0.008   0.022  -0.185   0.041
  -0.017   0.090  -0.194  -0.048   0.022   0.020   1.000   0.016   0.008
   0.044   0.116   0.155  -0.118
  -0.362  -0.041   0.251   0.140  -0.049   0.255   0.016   1.000  -0.025
  -0.035   0.033  -0.122   0.059
   0.091   0.035  -0.070  -0.112  -0.009  -0.057   0.008  -0.025   1.000
   0.051   0.034  -0.040  -0.048
   0.108   0.015  -0.117  -0.245   0.015  -0.008   0.044  -0.035   0.051
   1.000   0.162  -0.059  -0.156
   0.069  -0.144  -0.094  -0.209  -0.042   0.022   0.116   0.033   0.034
   0.162   1.000  -0.155  -0.916
   0.110   0.227  -0.176   0.112   0.047  -0.185   0.155  -0.122  -0.040
  -0.059  -0.155   1.000  -0.152
  -0.138   0.159   0.188   0.172  -0.001   0.041  -0.118   0.059  -0.048
  -0.156  -0.916  -0.152   1.000

Number of iterations    10
Minutes to convergence     0.02283

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
      0.17289122       0.79893410 
      0.11274428       0.17555137 
      0.26074559       0.58510230 
    -0.019001500     -0.041894379 
     0.019743666      0.042744827 
      0.16643431       0.87452874 
     0.064743701       0.44268985 
    -0.024566443     -0.062281768 
    -0.028266891     -0.068275752 

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
    0.0090251778     0.0057955054 
     0.017708330      0.035055949 
     0.078319357       0.20071561 
   -0.0010647708    -0.0024377042 
    0.0011062773     0.0023740212 
    0.0087315551    -0.0044760659 
    0.0035928655      0.011050745 
   -0.0013757533    -0.0037559930 
   -0.0015821910    -0.0041442421 
alpha= 1.41230 
beta=11.52379 
ave mean= 0.10918 
ave var= 0.00698 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.360      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.944      Std error of est:                 0.220
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.963429    0.229859   -4.191381     0.000       ---         ---  
X1           0.014216    0.009444    1.505231     0.140    0.189569    0.606581
X2           0.020866    0.027041    0.771619     0.445    0.086966    0.441778
X3           0.966330    0.239631    4.032584     0.000    0.467892    0.621866
X4          -0.044700    0.036695   -1.218141     0.230   -0.132979    0.008212
X5           0.034253    0.014661    2.336321     0.025    0.281867    0.453771
X6           0.821737    0.228384    3.598056     0.001    0.322567    0.313797
X7           0.166559    0.226446    0.735535     0.466    0.065381   -0.035959
X8          -0.215741    0.224952   -0.959052     0.343   -0.084688   -0.082752
X9          -0.530547    0.238320   -2.226191     0.032   -0.208262   -0.082752

 0.13659 
 0.06266 
 0.33713 
-0.09582 
 0.20310 
 0.23242 
 0.04711 
-0.06102 
-0.15006 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                 1189.472      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:               363.629      Std error of est:                 3.015
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -18.265392    3.143519   -5.810491     0.000       ---         ---  
X1           0.136142    0.129159    1.054058     0.298    0.132749    0.579444
X2           0.327376    0.369815    0.885244     0.381    0.099773    0.444637
X3          14.288819    3.277147    4.360140     0.000    0.505900    0.626741
X4          -0.541297    0.501841   -1.078622     0.287   -0.117749    0.020036
X5           0.478761    0.200501    2.387827     0.022    0.288083    0.449070
X6          11.174020    3.123337    3.577590     0.001    0.320734    0.315471
X7           3.296071    3.096835    1.064335     0.294    0.094609   -0.010946
X8          -3.332471    3.076409   -1.083234     0.285   -0.095654   -0.089295
X9          -7.897951    3.259231   -2.423256     0.020   -0.226699   -0.089295

 0.18973 
 0.14212 
 0.70115 
-0.16802 
 0.41723 
 0.46431 
 0.13470 
-0.13620 
-0.32728 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  161.930      Degrees of freedom:                  40
R-squared:                   0.811      Rbar-squared:                     0.768
Residual SS:                30.602      Std error of est:                 0.875
F(9,40):                    19.073      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.302264    3.399147   -4.501796     0.000       ---         ---  
X1           0.598213    0.268301    2.229634     0.031    0.253457    0.702647
X2           0.292582    0.107794    2.714263     0.010    0.241672    0.550418
X3           2.641677    0.496372    5.321974     0.000    0.468803    0.651090
X4          -0.502262    0.334016   -1.503707     0.141   -0.123646    0.077521
X5           1.893316    0.984129    1.923850     0.062    0.195191    0.456340
X6           2.710133    0.901357    3.006727     0.005    0.210834    0.245829
X7           2.330401    0.903376    2.579659     0.014    0.181293    0.081851
X8          -1.812607    0.897693   -2.019184     0.050   -0.141011   -0.120529
X9          -3.361353    0.920328   -3.652341     0.001   -0.261495   -0.120529

 0.04313 
 0.04100 
 0.08669 
-0.02049 
 0.03275 
 0.03549 
 0.03033 
-0.02342 
-0.04460 
-0.00654  1.42031 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00990  0.99990 
 0.00526  0.98159 
-0.18060  0.99990 
 0.00080  0.99990 
-0.00654  1.42031 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.26000 
 0.00000 
 0.00000 
 0.02000 
 0.16000 
Beta is better if rb/ro<1 0.87931 
Beta is better than logit trans if rb/ro<1 0.63403 
Beta is better if rb/rl<1 0.58075 

 0.00990  0.01768 -0.06902  0.00074 
 0.06138  0.23891  0.31153  0.07718 
 0.00990  0.03517  0.11977  0.02434 
 0.16236  0.40128  0.39186  0.18638 
 0.00990  0.00644 -0.01270 -0.00429 
 0.00990  0.00803 -0.11593 -0.00423 
 0.00990  0.02140 -0.03210  0.00321 
 0.00990  0.00843 -0.18060 -0.00509 
 0.00990  0.02388  0.12422  0.01229 
 0.00990  0.04376  0.00990  0.00000 
 0.00990  0.00526 -0.10089 -0.00578 
 0.00990  0.04793  0.12399  0.02085 
 0.08712  0.04226  0.03688  0.01676 
 0.00990  0.03231 -0.00763  0.00052 
 0.99990  0.51772  0.69950  0.30364 
 0.00990  0.06568  0.14586  0.00856 
 0.00990  0.01939  0.02169  0.00393 
 0.00990  0.01284  0.01761  0.00195 
 0.02772  0.07353  0.28736  0.04974 
 0.00990  0.02538  0.12305  0.01807 
 0.00990  0.04881  0.10548  0.01466 
 0.00990  0.02379 -0.01001  0.00908 
 0.00990  0.16420  0.29933  0.08092 
 0.00990  0.04338 -0.01861  0.01371 
 0.00990  0.01448 -0.00459  0.00231 
 0.99990  0.59018  0.56746  0.39720 
 0.00990  0.02558  0.00477  0.00824 
 0.00990  0.03152  0.09773  0.01618 
 0.00990  0.00940 -0.13053 -0.00654 
 0.00990  0.00841 -0.15264 -0.00522 
 0.00990  0.02371 -0.06331  0.00010 
 0.12672  0.12913  0.12672  0.11682 
 0.00990  0.43605  0.00990  0.00000 
 0.10098  0.15070  0.21493  0.05389 
 0.03267  0.02418  0.03258  0.00854 
 0.46035  0.26712  0.34868  0.15336 
 0.03663  0.01483  0.04136  0.00522 
 0.04851  0.06593  0.13151  0.02726 
 0.11484  0.54348  0.56182  0.31611 
 0.17721  0.18426  0.30070  0.11225 
 0.15147  0.35697  0.36603  0.16655 
 0.99990  0.50161  0.40743  0.22251 
 0.18513  0.30541  0.27408  0.13191 
 0.35739  0.41734  0.61225  0.22459 
 0.99990  0.77136  0.60645  0.27203 
 0.43758  0.98159  0.83379  0.97515 
 0.99990  0.97876  0.99990  0.99000 
 0.99990  0.83970  0.73863  0.76481 
 0.99990  0.96791  0.91198  1.42031 
 0.99990  0.69757  0.71653  0.43334 
dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/14/01  11:40 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         2.68585
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const           -8.6876        0.9298   -9.344   0.0000      0.0000
TASK             0.1046        0.0509    2.056   0.0199      0.0000
RIGHTS           0.3225        0.0975    3.307   0.0005      0.0000
ELITE            6.7305        0.9218    7.302   0.0000      0.0000
SAL             -0.1265        0.0985   -1.285   0.0995      0.0000
COL              0.0895        0.0513    1.747   0.0403      0.0000
WI               6.4033        1.0860    5.896   0.0000      0.0000
LA               2.3944        0.2592    9.237   0.0000      0.0000
DE              -0.9072        0.9599   -0.945   0.1723      0.0000
RI              -0.6030        1.4821   -0.407   0.3421      0.0000
const           10.3856        0.7717   13.458   0.0000      0.0000
TASK            -0.1383        0.0549   -2.520   0.0059      0.0000
RIGHTS          -0.4608        0.1325   -3.477   0.0003      0.0000
ELITE          -11.0507        1.2860   -8.593   0.0000      0.0000

Correlation matrix of the parameters
   1.000   0.413  -0.011  -0.662   0.359  -0.902   0.002  -0.381   0.092
   0.148   0.226   0.017   0.054  -0.265
   0.413   1.000  -0.070  -0.335   0.160  -0.524   0.028  -0.159   0.017
  -0.003  -0.094   0.135   0.140   0.039
  -0.011  -0.070   1.000   0.024  -0.198  -0.069  -0.243   0.237  -0.076
  -0.143  -0.149   0.180  -0.150   0.111
  -0.662  -0.335   0.024   1.000  -0.084   0.341  -0.118   0.170  -0.114
  -0.280  -0.349   0.221   0.091   0.202
   0.359   0.160  -0.198  -0.084   1.000  -0.447   0.005  -0.033  -0.025
   0.007  -0.003   0.043   0.050  -0.050
  -0.902  -0.524  -0.069   0.341  -0.447   1.000   0.050   0.304  -0.052
  -0.028  -0.090  -0.148  -0.112   0.199
   0.002   0.028  -0.243  -0.118   0.005   0.050   1.000   0.009   0.015
   0.070   0.156  -0.207   0.155  -0.061
  -0.381  -0.159   0.237   0.170  -0.033   0.304   0.009   1.000  -0.029
  -0.042  -0.008  -0.059  -0.096   0.093
   0.092   0.017  -0.076  -0.114  -0.025  -0.052   0.015  -0.029   1.000
   0.058   0.054  -0.005  -0.045  -0.058
   0.148  -0.003  -0.143  -0.280   0.007  -0.028   0.070  -0.042   0.058
   1.000   0.221  -0.078  -0.062  -0.169
   0.226  -0.094  -0.149  -0.349  -0.003  -0.090   0.156  -0.008   0.054
   0.221   1.000  -0.090  -0.157  -0.845
   0.017   0.135   0.180   0.221   0.043  -0.148  -0.207  -0.059  -0.005
  -0.078  -0.090   1.000  -0.162  -0.318
   0.054   0.140  -0.150   0.091   0.050  -0.112   0.155  -0.096  -0.045
  -0.062  -0.157  -0.162   1.000  -0.062
  -0.265   0.039   0.111   0.202  -0.050   0.199  -0.061   0.093  -0.058
  -0.169  -0.845  -0.318  -0.062   1.000

Number of iterations    6
Minutes to convergence     0.01491

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
     0.082611290       0.42665360 
     0.079501355       0.12247047 
      0.20947899       0.50063649 
    -0.021855543     -0.045258757 
     0.042995580      0.097397271 
      0.15554704       0.90242662 
     0.055045884       0.41843213 
    -0.020683284     -0.051477660 
    -0.013735634     -0.038360535 

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
     0.012026880       0.14141097 
     0.012201624      0.024304794 
     0.057266577       0.19228672 
   -0.0011355806    -0.0024424593 
    0.0022245992     0.0048787593 
    0.0075599144    -0.0033895237 
    0.0028378935      0.010908920 
   -0.0010748375    -0.0028365484 
  -0.00071432133    -0.0020843686 
alpha= 1.30876 
beta=13.51568 
ave mean= 0.08828 
ave var= 0.00509 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.360      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.944      Std error of est:                 0.220
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.963429    0.229859   -4.191381     0.000       ---         ---  
X1           0.014216    0.009444    1.505231     0.140    0.189569    0.606581
X2           0.020866    0.027041    0.771619     0.445    0.086966    0.441778
X3           0.966330    0.239631    4.032584     0.000    0.467892    0.621866
X4          -0.044700    0.036695   -1.218141     0.230   -0.132979    0.008212
X5           0.034253    0.014661    2.336321     0.025    0.281867    0.453771
X6           0.821737    0.228384    3.598056     0.001    0.322567    0.313797
X7           0.166559    0.226446    0.735535     0.466    0.065381   -0.035959
X8          -0.215741    0.224952   -0.959052     0.343   -0.084688   -0.082752
X9          -0.530547    0.238320   -2.226191     0.032   -0.208262   -0.082752

 0.13659 
 0.06266 
 0.33713 
-0.09582 
 0.20310 
 0.23242 
 0.04711 
-0.06102 
-0.15006 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                 1189.472      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:               363.629      Std error of est:                 3.015
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -18.265392    3.143519   -5.810491     0.000       ---         ---  
X1           0.136142    0.129159    1.054058     0.298    0.132749    0.579444
X2           0.327376    0.369815    0.885244     0.381    0.099773    0.444637
X3          14.288819    3.277147    4.360140     0.000    0.505900    0.626741
X4          -0.541297    0.501841   -1.078622     0.287   -0.117749    0.020036
X5           0.478761    0.200501    2.387827     0.022    0.288083    0.449070
X6          11.174020    3.123337    3.577590     0.001    0.320734    0.315471
X7           3.296071    3.096835    1.064335     0.294    0.094609   -0.010946
X8          -3.332471    3.076409   -1.083234     0.285   -0.095654   -0.089295
X9          -7.897951    3.259231   -2.423256     0.020   -0.226699   -0.089295

 0.18973 
 0.14212 
 0.70115 
-0.16802 
 0.41723 
 0.46431 
 0.13470 
-0.13620 
-0.32728 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  161.930      Degrees of freedom:                  40
R-squared:                   0.811      Rbar-squared:                     0.768
Residual SS:                30.602      Std error of est:                 0.875
F(9,40):                    19.073      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.302264    3.399147   -4.501796     0.000       ---         ---  
X1           0.598213    0.268301    2.229634     0.031    0.253457    0.702647
X2           0.292582    0.107794    2.714263     0.010    0.241672    0.550418
X3           2.641677    0.496372    5.321974     0.000    0.468803    0.651090
X4          -0.502262    0.334016   -1.503707     0.141   -0.123646    0.077521
X5           1.893316    0.984129    1.923850     0.062    0.195191    0.456340
X6           2.710133    0.901357    3.006727     0.005    0.210834    0.245829
X7           2.330401    0.903376    2.579659     0.014    0.181293    0.081851
X8          -1.812607    0.897693   -2.019184     0.050   -0.141011   -0.120529
X9          -3.361353    0.920328   -3.652341     0.001   -0.261495   -0.120529

 0.04313 
 0.04100 
 0.08669 
-0.02049 
 0.03275 
 0.03549 
 0.03033 
-0.02342 
-0.04460 
-0.00654  1.42031 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00990  0.99990 
 0.00635  0.98415 
-0.18060  0.99990 
 0.00080  0.99990 
-0.00654  1.42031 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.26000 
 0.00000 
 0.00000 
 0.02000 
 0.16000 
Beta is better if rb/ro<1 1.06547 
Beta is better than logit trans if rb/ro<1 0.76826 
Beta is better if rb/rl<1 0.70370 

 0.00990  0.01631 -0.06902  0.00074 
 0.06138  0.16911  0.31153  0.07718 
 0.00990  0.03537  0.11977  0.02434 
 0.16236  0.31281  0.39186  0.18638 
 0.00990  0.00901 -0.01270 -0.00429 
 0.00990  0.00838 -0.11593 -0.00423 
 0.00990  0.01771 -0.03210  0.00321 
 0.00990  0.00754 -0.18060 -0.00509 
 0.00990  0.02836  0.12422  0.01229 
 0.00990  0.03680  0.00990  0.00000 
 0.00990  0.00635 -0.10089 -0.00578 
 0.00990  0.03998  0.12399  0.02085 
 0.08712  0.03402  0.03688  0.01676 
 0.00990  0.02728 -0.00763  0.00052 
 0.99990  0.47754  0.69950  0.30364 
 0.00990  0.06324  0.14586  0.00856 
 0.00990  0.01978  0.02169  0.00393 
 0.00990  0.01264  0.01761  0.00195 
 0.02772  0.06199  0.28736  0.04974 
 0.00990  0.02452  0.12305  0.01807 
 0.00990  0.04279  0.10548  0.01466 
 0.00990  0.02186 -0.01001  0.00908 
 0.00990  0.13173  0.29933  0.08092 
 0.00990  0.03263 -0.01861  0.01371 
 0.00990  0.01497 -0.00459  0.00231 
 0.99990  0.46327  0.56746  0.39720 
 0.00990  0.02066  0.00477  0.00824 
 0.00990  0.03178  0.09773  0.01618 
 0.00990  0.00952 -0.13053 -0.00654 
 0.00990  0.00812 -0.15264 -0.00522 
 0.00990  0.01913 -0.06331  0.00010 
 0.12672  0.12850  0.12672  0.11682 
 0.00990  0.41021  0.00990  0.00000 
 0.10098  0.11452  0.21493  0.05389 
 0.03267  0.02093  0.03258  0.00854 
 0.46035  0.20294  0.34868  0.15336 
 0.03663  0.01593  0.04136  0.00522 
 0.04851  0.05371  0.13151  0.02726 
 0.11484  0.45635  0.56182  0.31611 
 0.17721  0.15154  0.30070  0.11225 
 0.15147  0.26854  0.36603  0.16655 
 0.99990  0.35458  0.40743  0.22251 
 0.18513  0.21178  0.27408  0.13191 
 0.35739  0.34112  0.61225  0.22459 
 0.99990  0.51793  0.60645  0.27203 
 0.43758  0.88823  0.83379  0.97515 
 0.99990  0.98415  0.99990  0.99000 
 0.99990  0.73512  0.73863  0.76481 
 0.99990  0.90796  0.91198  1.42031 
 0.99990  0.60105  0.71653  0.43334 
dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/14/01  11:46 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         1.94236
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const           -6.2979        1.3171   -4.782   0.0000      0.0000
TASK             0.1063        0.0613    1.734   0.0415      0.0000
RIGHTS           0.1534        0.1327    1.155   0.1240      0.0000
ELITE            4.7187        1.2473    3.783   0.0001      0.0000
SAL             -0.1808        0.1784   -1.013   0.1555      0.0000
COL              0.1377        0.0771    1.786   0.0370      0.0000
WI               3.4064        1.1406    2.987   0.0014      0.0000
LA               1.1227        1.1846    0.948   0.1716      0.0000
DE              -1.1192        1.1280   -0.992   0.1605      0.0000
RI              -2.8039        1.2136   -2.310   0.0104      0.0000
const            0.4704        0.2327    2.021   0.0216      0.0000

Correlation matrix of the parameters
   1.000   0.341  -0.036  -0.498   0.211  -0.818  -0.188  -0.169   0.070
   0.122  -0.421
   0.341   1.000  -0.109  -0.287   0.031  -0.460   0.122  -0.028   0.067
   0.042   0.310
  -0.036  -0.109   1.000  -0.148  -0.355   0.025  -0.154   0.084  -0.046
  -0.116   0.165
  -0.498  -0.287  -0.148   1.000   0.223   0.001   0.109   0.131  -0.053
  -0.339   0.315
   0.211   0.031  -0.355   0.223   1.000  -0.395   0.016   0.030  -0.060
  -0.074  -0.105
  -0.818  -0.460   0.025   0.001  -0.395   1.000   0.089   0.069  -0.061
   0.077   0.101
  -0.188   0.122  -0.154   0.109   0.016   0.089   1.000   0.036   0.007
  -0.010   0.261
  -0.169  -0.028   0.084   0.131   0.030   0.069   0.036   1.000  -0.003
  -0.044   0.093
   0.070   0.067  -0.046  -0.053  -0.060  -0.061   0.007  -0.003   1.000
   0.048  -0.074
   0.122   0.042  -0.116  -0.339  -0.074   0.077  -0.010  -0.044   0.048
   1.000  -0.212
  -0.421   0.310   0.165   0.315  -0.105   0.101   0.261   0.093  -0.074
  -0.212   1.000

Number of iterations    5
Minutes to convergence     0.00794

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
      0.22160397       0.60300336 
      0.10101437       0.13774534 
      0.34934052       0.63036829 
    -0.085065429      -0.18463585 
      0.17802205       0.37540677 
      0.20932212       0.61994948 
     0.069752998       0.27138809 
    -0.069538191      -0.19219610 
     -0.17298921      -0.30898262 
alpha= 0.52286 
beta= 1.07769 
ave mean= 0.32667 
ave var= 0.08458 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.360      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.944      Std error of est:                 0.220
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.963429    0.229859   -4.191381     0.000       ---         ---  
X1           0.014216    0.009444    1.505231     0.140    0.189569    0.606581
X2           0.020866    0.027041    0.771619     0.445    0.086966    0.441778
X3           0.966330    0.239631    4.032584     0.000    0.467892    0.621866
X4          -0.044700    0.036695   -1.218141     0.230   -0.132979    0.008212
X5           0.034253    0.014661    2.336321     0.025    0.281867    0.453771
X6           0.821737    0.228384    3.598056     0.001    0.322567    0.313797
X7           0.166559    0.226446    0.735535     0.466    0.065381   -0.035959
X8          -0.215741    0.224952   -0.959052     0.343   -0.084688   -0.082752
X9          -0.530547    0.238320   -2.226191     0.032   -0.208262   -0.082752

 0.13659 
 0.06266 
 0.33713 
-0.09582 
 0.20310 
 0.23242 
 0.04711 
-0.06102 
-0.15006 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                 1189.472      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:               363.629      Std error of est:                 3.015
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -18.265392    3.143519   -5.810491     0.000       ---         ---  
X1           0.136142    0.129159    1.054058     0.298    0.132749    0.579444
X2           0.327376    0.369815    0.885244     0.381    0.099773    0.444637
X3          14.288819    3.277147    4.360140     0.000    0.505900    0.626741
X4          -0.541297    0.501841   -1.078622     0.287   -0.117749    0.020036
X5           0.478761    0.200501    2.387827     0.022    0.288083    0.449070
X6          11.174020    3.123337    3.577590     0.001    0.320734    0.315471
X7           3.296071    3.096835    1.064335     0.294    0.094609   -0.010946
X8          -3.332471    3.076409   -1.083234     0.285   -0.095654   -0.089295
X9          -7.897951    3.259231   -2.423256     0.020   -0.226699   -0.089295

 0.18973 
 0.14212 
 0.70115 
-0.16802 
 0.41723 
 0.46431 
 0.13470 
-0.13620 
-0.32728 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  161.930      Degrees of freedom:                  40
R-squared:                   0.811      Rbar-squared:                     0.768
Residual SS:                30.602      Std error of est:                 0.875
F(9,40):                    19.073      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.302264    3.399147   -4.501796     0.000       ---         ---  
X1           0.598213    0.268301    2.229634     0.031    0.253457    0.702647
X2           0.292582    0.107794    2.714263     0.010    0.241672    0.550418
X3           2.641677    0.496372    5.321974     0.000    0.468803    0.651090
X4          -0.502262    0.334016   -1.503707     0.141   -0.123646    0.077521
X5           1.893316    0.984129    1.923850     0.062    0.195191    0.456340
X6           2.710133    0.901357    3.006727     0.005    0.210834    0.245829
X7           2.330401    0.903376    2.579659     0.014    0.181293    0.081851
X8          -1.812607    0.897693   -2.019184     0.050   -0.141011   -0.120529
X9          -3.361353    0.920328   -3.652341     0.001   -0.261495   -0.120529

 0.04313 
 0.04100 
 0.08669 
-0.02049 
 0.03275 
 0.03549 
 0.03033 
-0.02342 
-0.04460 
-0.00654  1.42031 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00990  0.99990 
 0.06078  0.95937 
-0.18060  0.99990 
 0.00080  0.99990 
-0.00654  1.42031 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.26000 
 0.00000 
 0.00000 
 0.02000 
 0.16000 
Beta is better if rb/ro<1 1.37832 
Beta is better than logit trans if rb/ro<1 0.99384 
Beta is better if rb/rl<1 0.91032 

 0.00990  0.10786 -0.06902  0.00074 
 0.06138  0.45222  0.31153  0.07718 
 0.00990  0.21433  0.11977  0.02434 
 0.16236  0.56776  0.39186  0.18638 
 0.00990  0.10750 -0.01270 -0.00429 
 0.00990  0.07568 -0.11593 -0.00423 
 0.00990  0.12394 -0.03210  0.00321 
 0.00990  0.06078 -0.18060 -0.00509 
 0.00990  0.19892  0.12422  0.01229 
 0.00990  0.14087  0.00990  0.00000 
 0.00990  0.07872 -0.10089 -0.00578 
 0.00990  0.22547  0.12399  0.02085 
 0.08712  0.17082  0.03688  0.01676 
 0.00990  0.13067 -0.00763  0.00052 
 0.99990  0.81628  0.69950  0.30364 
 0.00990  0.23591  0.14586  0.00856 
 0.00990  0.13722  0.02169  0.00393 
 0.00990  0.14379  0.01761  0.00195 
 0.02772  0.39179  0.28736  0.04974 
 0.00990  0.21279  0.12305  0.01807 
 0.00990  0.20299  0.10548  0.01466 
 0.00990  0.14487 -0.01001  0.00908 
 0.00990  0.42737  0.29933  0.08092 
 0.00990  0.14320 -0.01861  0.01371 
 0.00990  0.12362 -0.00459  0.00231 
 0.99990  0.75486  0.56746  0.39720 
 0.00990  0.14288  0.00477  0.00824 
 0.00990  0.19166  0.09773  0.01618 
 0.00990  0.07186 -0.13053 -0.00654 
 0.00990  0.06671 -0.15264 -0.00522 
 0.00990  0.10666 -0.06331  0.00010 
 0.12672  0.27687  0.12672  0.11682 
 0.00990  0.14087  0.00990  0.00000 
 0.10098  0.33348  0.21493  0.05389 
 0.03267  0.15654  0.03258  0.00854 
 0.46035  0.49952  0.34868  0.15336 
 0.03663  0.14789  0.04136  0.00522 
 0.04851  0.23793  0.13151  0.02726 
 0.11484  0.73519  0.56182  0.31611 
 0.17721  0.45527  0.30070  0.11225 
 0.15147  0.52368  0.36603  0.16655 
 0.99990  0.61336  0.40743  0.22251 
 0.18513  0.43248  0.27408  0.13191 
 0.35739  0.76374  0.61225  0.22459 
 0.99990  0.83917  0.60645  0.27203 
 0.43758  0.95937  0.83379  0.97515 
 0.99990  0.92889  0.99990  0.99000 
 0.99990  0.88559  0.73863  0.76481 
 0.99990  0.95757  0.91198  1.42031 
 0.99990  0.84972  0.71653  0.43334 
dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/16/01   4:55 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         2.61712
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const           -8.2138        0.9441   -8.700   0.0000      0.0000
TASK             0.1768        0.0472    3.745   0.0001      0.0000
RIGHTS           0.3778        0.1002    3.770   0.0001      0.0000
ELITE            7.0489        0.8864    7.952   0.0000      0.0000
SAL             -0.0911        0.0957   -0.951   0.1707      0.0000
COL              0.0342        0.0539    0.635   0.2628      0.0000
WI               5.7970        1.0707    5.414   0.0000      0.0000
LA               2.3361        0.2960    7.891   0.0000      0.0000
DE              -0.8921        0.9804   -0.910   0.1814      0.0000
RI              -1.0261        1.4755   -0.695   0.2434      0.0000
const            9.9657        0.7437   13.400   0.0000      0.0000
RIGHTS          -0.4755        0.1387   -3.427   0.0003      0.0000
ELITE          -11.8178        1.2171   -9.710   0.0000      0.0000

Correlation matrix of the parameters
   1.000   0.454  -0.004  -0.612   0.331  -0.904  -0.018  -0.364   0.092
   0.107   0.076   0.109  -0.146
   0.454   1.000   0.019  -0.381   0.111  -0.568   0.092  -0.034   0.034
   0.013  -0.143   0.226   0.159
  -0.004   0.019   1.000  -0.091  -0.289  -0.054  -0.195   0.252  -0.071
  -0.116  -0.094  -0.180   0.188
  -0.612  -0.381  -0.091   1.000  -0.045   0.302  -0.048   0.135  -0.112
  -0.245  -0.213   0.118   0.174
   0.331   0.111  -0.289  -0.045   1.000  -0.398   0.023  -0.044  -0.009
   0.012  -0.038   0.046  -0.005
  -0.904  -0.568  -0.054   0.302  -0.398   1.000   0.021   0.256  -0.057
  -0.005   0.017  -0.187   0.047
  -0.018   0.092  -0.195  -0.048   0.023   0.021   1.000   0.017   0.008
   0.044   0.116   0.155  -0.118
  -0.364  -0.034   0.252   0.135  -0.044   0.256   0.017   1.000  -0.025
  -0.034   0.032  -0.123   0.061
   0.092   0.034  -0.071  -0.112  -0.009  -0.057   0.008  -0.025   1.000
   0.051   0.034  -0.040  -0.049
   0.107   0.013  -0.116  -0.245   0.012  -0.005   0.044  -0.034   0.051
   1.000   0.162  -0.060  -0.156
   0.076  -0.143  -0.094  -0.213  -0.038   0.017   0.116   0.032   0.034
   0.162   1.000  -0.155  -0.916
   0.109   0.226  -0.180   0.118   0.046  -0.187   0.155  -0.123  -0.040
  -0.060  -0.155   1.000  -0.153
  -0.146   0.159   0.188   0.174  -0.005   0.047  -0.118   0.061  -0.049
  -0.156  -0.916  -0.153   1.000

Number of iterations    5
Minutes to convergence     0.02093

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
      0.17289152       0.79893492 
      0.11274431       0.17555142 
      0.26074549       0.58510206 
    -0.019001404     -0.041894199 
     0.019743355      0.042744141 
      0.16643432       0.87452873 
     0.064743687       0.44268969 
    -0.024566433     -0.062281755 
    -0.028266890     -0.068275755 

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
    0.0088824840     0.0026261767     0.0064434465     0.0048891613 
     0.018407273     0.0060246550      0.036925540      0.013931301 
     0.076859243      0.014049512       0.19173640      0.023602662 
   -0.0010989066     0.0011417350    -0.0022437849     0.0023716454 
    0.0012490984     0.0018030085     0.0027003712     0.0038277421 
    0.0087391467     0.0021590135    -0.0036814921     0.0028402126 
    0.0036152105    0.00079514046      0.010742888     0.0021779648 
   -0.0013263328     0.0015136634    -0.0027047332     0.0036062941 
   -0.0015025122     0.0023551420    -0.0022123455     0.0050602703 
alpha= 1.41230 
beta=11.52379 
ave mean= 0.10918 
ave var= 0.00698 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.360      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.944      Std error of est:                 0.220
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.963429    0.229859   -4.191381     0.000       ---         ---  
X1           0.014216    0.009444    1.505231     0.140    0.189569    0.606581
X2           0.020866    0.027041    0.771619     0.445    0.086966    0.441778
X3           0.966330    0.239631    4.032584     0.000    0.467892    0.621866
X4          -0.044700    0.036695   -1.218141     0.230   -0.132979    0.008212
X5           0.034253    0.014661    2.336321     0.025    0.281867    0.453771
X6           0.821737    0.228384    3.598056     0.001    0.322567    0.313797
X7           0.166559    0.226446    0.735535     0.466    0.065381   -0.035959
X8          -0.215741    0.224952   -0.959052     0.343   -0.084688   -0.082752
X9          -0.530547    0.238320   -2.226191     0.032   -0.208262   -0.082752

 0.13659 
 0.06266 
 0.33713 
-0.09582 
 0.20310 
 0.23242 
 0.04711 
-0.06102 
-0.15006 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                 1189.472      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:               363.629      Std error of est:                 3.015
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -18.265392    3.143519   -5.810491     0.000       ---         ---  
X1           0.136142    0.129159    1.054058     0.298    0.132749    0.579444
X2           0.327376    0.369815    0.885244     0.381    0.099773    0.444637
X3          14.288819    3.277147    4.360140     0.000    0.505900    0.626741
X4          -0.541297    0.501841   -1.078622     0.287   -0.117749    0.020036
X5           0.478761    0.200501    2.387827     0.022    0.288083    0.449070
X6          11.174020    3.123337    3.577590     0.001    0.320734    0.315471
X7           3.296071    3.096835    1.064335     0.294    0.094609   -0.010946
X8          -3.332471    3.076409   -1.083234     0.285   -0.095654   -0.089295
X9          -7.897951    3.259231   -2.423256     0.020   -0.226699   -0.089295

 0.18973 
 0.14212 
 0.70115 
-0.16802 
 0.41723 
 0.46431 
 0.13470 
-0.13620 
-0.32728 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  202.870      Degrees of freedom:                  44
R-squared:                   0.611      Rbar-squared:                     0.567
Residual SS:                78.897      Std error of est:                 1.339
F(5,44):                    13.828      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.437198    5.732646   -2.692858     0.010       ---         ---  
X1           0.914732    0.399571    2.289285     0.027    0.346257    0.704605
X2           0.853768    0.929137    0.918883     0.363    0.095548    0.335304
X3           0.190633    0.153481    1.242064     0.221    0.140680    0.510757
X4           1.874436    0.793981    2.360808     0.023    0.297192    0.611638
X5           1.734884    1.389473    1.248591     0.218    0.159794    0.509765

 0.16651 
 0.04262 
 0.06322 
 0.13992 
 0.07209 
-0.00341  2.70982 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00990  0.99990 
 0.00526  0.98159 
-0.18060  0.99990 
 0.00080  0.99990 
-0.00341  2.70982 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.26000 
 0.00000 
 0.00000 
 0.08000 
 0.06000 
Beta is better if rb/ro<1 0.87931 
Beta is better than logit trans if rb/ro<1 0.63403 
Beta is better if rb/rl<1 0.14143 

 0.00990  0.01768 -0.06902  0.00404 
 0.06138  0.23891  0.31153  0.46378 
 0.00990  0.03517  0.11977  0.05213 
 0.16236  0.40128  0.39186  0.77071 
 0.00990  0.00644 -0.01270  0.00925 
 0.00990  0.00803 -0.11593  0.00200 
 0.00990  0.02140 -0.03210  0.00662 
 0.00990  0.00843 -0.18060  0.00080 
 0.00990  0.02388  0.12422  0.05907 
 0.00990  0.04376  0.00990  0.00990 
 0.00990  0.00526 -0.10089  0.00216 
 0.00990  0.04793  0.12399  0.05354 
 0.08712  0.04226  0.03688  0.01748 
 0.00990  0.03231 -0.00763  0.01092 
 0.99990  0.51772  0.69950  0.99463 
 0.00990  0.06568  0.14586  0.10593 
 0.00990  0.01939  0.02169  0.01460 
 0.00990  0.01284  0.01761  0.00933 
 0.02772  0.07353  0.28736  0.29559 
 0.00990  0.02538  0.12305  0.04392 
 0.00990  0.04881  0.10548  0.04855 
 0.00990  0.02379 -0.01001  0.01179 
 0.00990  0.16420  0.29933  0.42545 
 0.00990  0.04338 -0.01861  0.00840 
 0.00990  0.01448 -0.00459  0.00946 
 0.99990  0.59018  0.56746  0.96362 
 0.00990  0.02558  0.00477  0.00972 
 0.00990  0.03152  0.09773  0.04099 
 0.00990  0.00940 -0.13053  0.00186 
 0.00990  0.00841 -0.15264  0.00124 
 0.00990  0.02371 -0.06331  0.00465 
 0.12672  0.12913  0.12672  0.12672 
 0.00990  0.43605  0.00990  0.00990 
 0.10098  0.15070  0.21493  0.20050 
 0.03267  0.02418  0.03258  0.01438 
 0.46035  0.26712  0.34868  0.58668 
 0.03663  0.01483  0.04136  0.01651 
 0.04851  0.06593  0.13151  0.06508 
 0.11484  0.54348  0.56182  0.96832 
 0.17721  0.18426  0.30070  0.47769 
 0.15147  0.35697  0.36603  0.67129 
 0.99990  0.50161  0.40743  0.77720 
 0.18513  0.30541  0.27408  0.35919 
 0.35739  0.41734  0.61225  0.97695 
 0.99990  0.77136  0.60645  0.96150 
 0.43758  0.98159  0.83379  0.99733 
 0.99990  0.97876  0.99990  0.99990 
 0.99990  0.83969  0.73863  0.99667 
 0.99990  0.96791  0.91198  0.99959 
 0.99990  0.69757  0.71653  0.99547 
dependent variable=             PVT 
vector of parameter labels does not conform to vector of starting values

Line 104 in betasim.dir.prg
Line 2962 in /usr/local/gauss/src/cmlutil.src
   Matrices are not conformable G0036
Currently active call: _cml_grdcd [2962]
dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/17/01   9:18 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         1.94236
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const           -6.2979        1.3167   -4.783   0.0000      0.0000
TASK             0.1063        0.0613    1.733   0.0415      0.0000
RIGHTS           0.1534        0.1328    1.155   0.1241      0.0000
ELITE            4.7187        1.2474    3.783   0.0001      0.0000
SAL             -0.1808        0.1786   -1.012   0.1557      0.0000
COL              0.1377        0.0771    1.786   0.0370      0.0000
WI               3.4064        1.1406    2.987   0.0014      0.0000
LA               1.1227        1.1842    0.948   0.1715      0.0000
DE              -1.1192        1.1280   -0.992   0.1606      0.0000
RI              -2.8039        1.2136   -2.310   0.0104      0.0000
const            0.4704        0.2327    2.022   0.0216      0.0000

Correlation matrix of the parameters
   1.000   0.341  -0.036  -0.498   0.211  -0.818  -0.188  -0.168   0.070
   0.122  -0.421
   0.341   1.000  -0.108  -0.287   0.031  -0.460   0.122  -0.028   0.068
   0.042   0.310
  -0.036  -0.108   1.000  -0.148  -0.356   0.026  -0.154   0.084  -0.046
  -0.116   0.165
  -0.498  -0.287  -0.148   1.000   0.223   0.000   0.109   0.130  -0.053
  -0.339   0.315
   0.211   0.031  -0.356   0.223   1.000  -0.394   0.016   0.029  -0.060
  -0.074  -0.106
  -0.818  -0.460   0.026   0.000  -0.394   1.000   0.089   0.069  -0.062
   0.077   0.101
  -0.188   0.122  -0.154   0.109   0.016   0.089   1.000   0.036   0.007
  -0.010   0.261
  -0.168  -0.028   0.084   0.130   0.029   0.069   0.036   1.000  -0.003
  -0.044   0.093
   0.070   0.068  -0.046  -0.053  -0.060  -0.062   0.007  -0.003   1.000
   0.048  -0.074
   0.122   0.042  -0.116  -0.339  -0.074   0.077  -0.010  -0.044   0.048
   1.000  -0.212
  -0.421   0.310   0.165   0.315  -0.106   0.101   0.261   0.093  -0.074
  -0.212   1.000

Number of iterations    3
Minutes to convergence     0.00513

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
      0.22160397       0.60300336 
      0.10101431       0.13774525 
      0.34934053       0.63036831 
    -0.085065340      -0.18463570 
      0.17802201       0.37540668 
      0.20932212       0.61994947 
     0.069752993       0.27138807 
    -0.069538178      -0.19219607 
     -0.17298920      -0.30898262 

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
     0.025610057      0.013264561     -0.014360893      0.023039655 
     0.012946769      0.011077375      0.014090122      0.012091986 
     0.038123005     0.0096794202      0.042379612      0.010084087 
    -0.010309699      0.010079121     -0.030805882      0.025836574 
     0.020457040      0.012253460      0.029874602      0.015504115 
     0.025321878     0.0081220777     -0.051308269      0.024227959 
    0.0089484830     0.0091339318    -0.0094051028      0.021796129 
   -0.0091503114     0.0093008813     -0.036686524      0.029257953 
    -0.020669471     0.0090027290     -0.066732939      0.020599191 
alpha= 0.52286 
beta= 1.07769 
ave mean= 0.32667 
ave var= 0.08458 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.360      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.944      Std error of est:                 0.220
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.963429    0.229859   -4.191381     0.000       ---         ---  
X1           0.014216    0.009444    1.505231     0.140    0.189569    0.606581
X2           0.020866    0.027041    0.771619     0.445    0.086966    0.441778
X3           0.966330    0.239631    4.032584     0.000    0.467892    0.621866
X4          -0.044700    0.036695   -1.218141     0.230   -0.132979    0.008212
X5           0.034253    0.014661    2.336321     0.025    0.281867    0.453771
X6           0.821737    0.228384    3.598056     0.001    0.322567    0.313797
X7           0.166559    0.226446    0.735535     0.466    0.065381   -0.035959
X8          -0.215741    0.224952   -0.959052     0.343   -0.084688   -0.082752
X9          -0.530547    0.238320   -2.226191     0.032   -0.208262   -0.082752

 0.13659 
 0.06266 
 0.33713 
-0.09582 
 0.20310 
 0.23242 
 0.04711 
-0.06102 
-0.15006 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                 1189.472      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:               363.629      Std error of est:                 3.015
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -18.265392    3.143519   -5.810491     0.000       ---         ---  
X1           0.136142    0.129159    1.054058     0.298    0.132749    0.579444
X2           0.327376    0.369815    0.885244     0.381    0.099773    0.444637
X3          14.288819    3.277147    4.360140     0.000    0.505900    0.626741
X4          -0.541297    0.501841   -1.078622     0.287   -0.117749    0.020036
X5           0.478761    0.200501    2.387827     0.022    0.288083    0.449070
X6          11.174020    3.123337    3.577590     0.001    0.320734    0.315471
X7           3.296071    3.096835    1.064335     0.294    0.094609   -0.010946
X8          -3.332471    3.076409   -1.083234     0.285   -0.095654   -0.089295
X9          -7.897951    3.259231   -2.423256     0.020   -0.226699   -0.089295

 0.18973 
 0.14212 
 0.70115 
-0.16802 
 0.41723 
 0.46431 
 0.13470 
-0.13620 
-0.32728 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  202.870      Degrees of freedom:                  44
R-squared:                   0.611      Rbar-squared:                     0.567
Residual SS:                78.897      Std error of est:                 1.339
F(5,44):                    13.828      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.437198    5.732646   -2.692858     0.010       ---         ---  
X1           0.914732    0.399571    2.289285     0.027    0.346257    0.704605
X2           0.853768    0.929137    0.918883     0.363    0.095548    0.335304
X3           0.190633    0.153481    1.242064     0.221    0.140680    0.510757
X4           1.874436    0.793981    2.360808     0.023    0.297192    0.611638
X5           1.734884    1.389473    1.248591     0.218    0.159794    0.509765

 0.16651 
 0.04262 
 0.06322 
 0.13992 
 0.07209 
-0.00341  2.70982 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00990  0.99990 
 0.06078  0.95937 
-0.18060  0.99990 
 0.00080  0.99990 
-0.00341  2.70982 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.26000 
 0.00000 
 0.00000 
 0.08000 
 0.06000 
Beta is better if rb/ro<1 1.37832 
Beta is better than logit trans if rb/ro<1 0.99384 
Beta is better if rb/rl<1 0.22168 

 0.00990  0.10786 -0.06902  0.00404 
 0.06138  0.45222  0.31153  0.46378 
 0.00990  0.21433  0.11977  0.05213 
 0.16236  0.56776  0.39186  0.77071 
 0.00990  0.10750 -0.01270  0.00925 
 0.00990  0.07568 -0.11593  0.00200 
 0.00990  0.12394 -0.03210  0.00662 
 0.00990  0.06078 -0.18060  0.00080 
 0.00990  0.19892  0.12422  0.05907 
 0.00990  0.14087  0.00990  0.00990 
 0.00990  0.07872 -0.10089  0.00216 
 0.00990  0.22547  0.12399  0.05354 
 0.08712  0.17082  0.03688  0.01748 
 0.00990  0.13067 -0.00763  0.01092 
 0.99990  0.81628  0.69950  0.99463 
 0.00990  0.23591  0.14586  0.10593 
 0.00990  0.13722  0.02169  0.01460 
 0.00990  0.14379  0.01761  0.00933 
 0.02772  0.39179  0.28736  0.29559 
 0.00990  0.21279  0.12305  0.04392 
 0.00990  0.20299  0.10548  0.04855 
 0.00990  0.14487 -0.01001  0.01179 
 0.00990  0.42737  0.29933  0.42545 
 0.00990  0.14320 -0.01861  0.00840 
 0.00990  0.12362 -0.00459  0.00946 
 0.99990  0.75486  0.56746  0.96362 
 0.00990  0.14288  0.00477  0.00972 
 0.00990  0.19166  0.09773  0.04099 
 0.00990  0.07186 -0.13053  0.00186 
 0.00990  0.06671 -0.15264  0.00124 
 0.00990  0.10666 -0.06331  0.00465 
 0.12672  0.27687  0.12672  0.12672 
 0.00990  0.14087  0.00990  0.00990 
 0.10098  0.33348  0.21493  0.20050 
 0.03267  0.15654  0.03258  0.01438 
 0.46035  0.49952  0.34868  0.58668 
 0.03663  0.14789  0.04136  0.01651 
 0.04851  0.23793  0.13151  0.06508 
 0.11484  0.73519  0.56182  0.96832 
 0.17721  0.45527  0.30070  0.47769 
 0.15147  0.52368  0.36603  0.67129 
 0.99990  0.61336  0.40743  0.77720 
 0.18513  0.43248  0.27408  0.35919 
 0.35739  0.76374  0.61225  0.97695 
 0.99990  0.83917  0.60645  0.96150 
 0.43758  0.95937  0.83379  0.99733 
 0.99990  0.92889  0.99990  0.99990 
 0.99990  0.88559  0.73863  0.99667 
 0.99990  0.95757  0.91198  0.99959 
 0.99990  0.84972  0.71653  0.99547 
dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/20/01   9:01 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         3.94237
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const           -6.6721        1.3865   -4.812   0.0000      0.0000
TASK             0.1032        0.0632    1.632   0.0513      0.0000
RIGHTS           0.1772        0.1373    1.291   0.0983      0.0000
ELITE            4.9268        1.2873    3.827   0.0001      0.0000
SAL             -0.1794        0.1773   -1.012   0.1558      0.0000
COL              0.1338        0.0778    1.719   0.0428      0.0000
WI               3.3324        1.1793    2.826   0.0024      0.0000
LA               1.6236        1.2549    1.294   0.0979      0.0000
DE              -1.2645        1.1164   -1.133   0.1287      0.0000
RI              -3.0457        1.2177   -2.501   0.0062      0.0000
const            0.1049        0.2486    0.422   0.3365      0.0000

Correlation matrix of the parameters
   1.000   0.300  -0.030  -0.550   0.235  -0.813  -0.210  -0.170   0.086
   0.162  -0.477
   0.300   1.000  -0.100  -0.268   0.047  -0.451   0.131  -0.018   0.056
   0.025   0.326
  -0.030  -0.100   1.000  -0.109  -0.320  -0.009  -0.154   0.087  -0.059
  -0.146   0.174
  -0.550  -0.268  -0.109   1.000   0.163   0.058   0.125   0.136  -0.068
  -0.364   0.366
   0.235   0.047  -0.320   0.163   1.000  -0.403   0.005   0.022  -0.055
  -0.056  -0.119
  -0.813  -0.451  -0.009   0.058  -0.403   1.000   0.102   0.070  -0.065
   0.059   0.123
  -0.210   0.131  -0.154   0.125   0.005   0.102   1.000   0.042   0.001
  -0.022   0.285
  -0.170  -0.018   0.087   0.136   0.022   0.070   0.042   1.000  -0.009
  -0.054   0.115
   0.086   0.056  -0.059  -0.068  -0.055  -0.065   0.001  -0.009   1.000
   0.060  -0.095
   0.162   0.025  -0.146  -0.364  -0.056   0.059  -0.022  -0.054   0.060
   1.000  -0.252
  -0.477   0.326   0.174   0.366  -0.119   0.123   0.285   0.115  -0.095
  -0.252   1.000

Number of iterations    6
Minutes to convergence     0.01434

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
      0.19153479       0.59031102 
      0.10335888       0.14316308 
      0.32717043       0.60853237 
    -0.074754944      -0.15674026 
      0.15365770       0.33164732 
      0.18222977       0.65227842 
     0.089219528       0.38018670 
    -0.069524338      -0.17515387 
     -0.16672913      -0.25871822 

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
     0.037471360      0.021449306     0.0012507189      0.028475328 
     0.020743812      0.015784971      0.024659164      0.018076532 
     0.059519928      0.012289244      0.070229803      0.012348538 
    -0.015886416      0.015113192     -0.039214213      0.032689882 
     0.031097224      0.018025003      0.049374568      0.023942586 
     0.037453028      0.012010561     -0.041544232      0.032999736 
     0.019447028      0.014399460    -0.0049523794      0.031677840 
    -0.014893964      0.012926479     -0.045368674      0.033278011 
    -0.033794215      0.012864820     -0.079522242      0.021822266 
alpha= 0.29381 
beta= 0.81677 
ave mean= 0.26456 
ave var= 0.09219 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.486      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.983      Std error of est:                 0.223
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.982863    0.232135   -4.234020     0.000       ---         ---  
X1           0.014357    0.009538    1.505231     0.140    0.189569    0.606581
X2           0.021072    0.027309    0.771619     0.445    0.086966    0.441778
X3           0.975895    0.242002    4.032584     0.000    0.467892    0.621866
X4          -0.045143    0.037059   -1.218141     0.230   -0.132979    0.008212
X5           0.034592    0.014806    2.336321     0.025    0.281867    0.453771
X6           0.829871    0.230644    3.598056     0.001    0.322567    0.313797
X7           0.168207    0.228687    0.735535     0.466    0.065381   -0.035959
X8          -0.217876    0.227179   -0.959052     0.343   -0.084688   -0.082752
X9          -0.535798    0.240679   -2.226191     0.032   -0.208262   -0.082752

 0.13794 
 0.06328 
 0.34047 
-0.09676 
 0.20511 
 0.23472 
 0.04758 
-0.06162 
-0.15155 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                 2177.498      Degrees of freedom:                  40
R-squared:                   0.763      Rbar-squared:                     0.710
Residual SS:               515.180      Std error of est:                 3.589
F(9,40):                    14.341      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -27.065860    3.741677   -7.233618     0.000       ---         ---  
X1           0.182558    0.153736    1.187478     0.242    0.131565    0.610722
X2           0.674086    0.440184    1.531372     0.134    0.151837    0.485433
X3          20.649065    3.900732    5.293639     0.000    0.540340    0.659039
X4          -0.688691    0.597333   -1.152944     0.256   -0.110724    0.025887
X5           0.610057    0.238653    2.556254     0.014    0.271311    0.459219
X6          13.313469    3.717654    3.581148     0.001    0.282439    0.285778
X7           7.393776    3.686110    2.005848     0.052    0.156856    0.042996
X8          -5.750007    3.661796   -1.570269     0.124   -0.121984   -0.112859
X9         -12.652946    3.879406   -3.261568     0.002   -0.268427   -0.112859

 0.03471 
 0.04149 
 0.40203 
-0.02830 
 0.09780 
 0.10494 
 0.04326 
-0.03170 
-0.09601 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  202.870      Degrees of freedom:                  44
R-squared:                   0.611      Rbar-squared:                     0.567
Residual SS:                78.897      Std error of est:                 1.339
F(5,44):                    13.828      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.437198    5.732646   -2.692858     0.010       ---         ---  
X1           0.914732    0.399571    2.289285     0.027    0.346257    0.704605
X2           0.853768    0.929137    0.918883     0.363    0.095548    0.335304
X3           0.190633    0.153481    1.242064     0.221    0.140680    0.510757
X4           1.874436    0.793981    2.360808     0.023    0.297192    0.611638
X5           1.734884    1.389473    1.248591     0.218    0.159794    0.509765

 0.16651 
 0.04262 
 0.06322 
 0.13992 
 0.07209 
-0.00341  2.70982 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00010  0.99990 
 0.04394  0.94777 
-0.19229  0.99990 
 0.00001  0.99993 
-0.00341  2.70982 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.28000 
 0.00000 
 0.00000 
 0.08000 
 0.06000 
Beta is better if rb/ro<1 1.13640 
beta mse= 0.04507 
ols mse= 0.03966 
Beta is better than logit trans if rb/ro<1 1.16947 
Beta is better if rb/rl<1 0.18641 

 0.00010  0.08158 -0.07961  0.00009 
 0.05209  0.38617  0.30472  0.13391 
 0.00010  0.16636  0.11106  0.00275 
 0.15407  0.51394  0.38584  0.63258 
 0.00010  0.07571 -0.02272  0.00013 
 0.00010  0.05444 -0.12698  0.00002 
 0.00010  0.09110 -0.04232  0.00012 
 0.00010  0.04394 -0.19229  0.00001 
 0.00010  0.15168  0.11555  0.00267 
 0.00010  0.09612  0.00010  0.00010 
 0.00010  0.05534 -0.11179  0.00002 
 0.00010  0.17332  0.11532  0.00238 
 0.07808  0.13308  0.02734  0.00072 
 0.00010  0.10081 -0.01760  0.00032 
 0.99990  0.76863  0.69653  0.99401 
 0.00010  0.19049  0.13741  0.00967 
 0.00010  0.10253  0.01201  0.00036 
 0.00010  0.10260  0.00789  0.00015 
 0.01810  0.30834  0.28031  0.02729 
 0.00010  0.15729  0.11437  0.00133 
 0.00010  0.15868  0.09662  0.00239 
 0.00010  0.10766 -0.02000  0.00035 
 0.00010  0.36001  0.29239  0.10928 
 0.00010  0.11322 -0.02869  0.00033 
 0.00010  0.09039 -0.01453  0.00018 
 0.99990  0.70634  0.56318  0.95507 
 0.00010  0.10600 -0.00508  0.00021 
 0.00010  0.14744  0.08880  0.00179 
 0.00010  0.05257 -0.14172  0.00002 
 0.00010  0.04825 -0.16405  0.00001 
 0.00010  0.08042 -0.07384  0.00009 
 0.11808  0.30767  0.11808  0.11808 
 0.00010  0.09612  0.00010  0.00010 
 0.09208  0.27985  0.20716  0.03270 
 0.02310  0.11558  0.02300  0.00033 
 0.45501  0.43750  0.34223  0.27901 
 0.02709  0.10741  0.03187  0.00034 
 0.03909  0.18868  0.12291  0.00417 
 0.10608  0.68702  0.55748  0.96451 
 0.16907  0.38803  0.29378  0.17560 
 0.14307  0.46879  0.35975  0.43287 
 0.99990  0.55875  0.40156  0.64436 
 0.17706  0.38192  0.26689  0.13505 
 0.35103  0.70006  0.60841  0.95036 
 0.99990  0.79118  0.60256  0.93421 
 0.43201  0.94712  0.83215  0.99896 
 0.99990  0.90382  0.99990  0.99990 
 0.99990  0.86109  0.73604  0.99865 
 0.99990  0.94777  0.91111  0.99993 
 0.99990  0.81274  0.71373  0.99646 

code used to generate the above results:

library cml;
#include cml.ext;
CMLset;

__title=" ** A Beta Model, Numerical Solution **";
dta="/home/gov/faculty/ppaolino/parr/gaydata1";
let dep=pvt;
let ind=task rights elite sal col wi la de ri;
let indV=0;
let sel=0;

c={1,0,0,0,0,0,0,0,0,0};

if ind==0;
   vars=dep;
   elseif indV==0; 
   vars=dep|ind;    
   else;
   vars=dep|ind|indV;
endif;

dataset=listw(dta,vars,sel);

stval=  -6.2979|
	 0.1063|
	 0.1534|
	 4.7187|
	-0.1808|
	 0.1377|
	 3.4064|
	 1.1227|
	-1.1192|
	-2.8039|
	 0.4704;
	 
proc psi(x);
  local p;
  x=x+6;
  p=1/(x.*x);
  p=(((0.004166666666667*p-0.003968253986254).*p+
      0.008333333333333).*p-0.083333333333333).*p;
  p=p+ln(x)-0.5/x-1/(x-1)-1/(x-2)-1/(x-3)-1/(x-4)-1/(x-5)-1/(x-6);
retp(p);
endp;

proc gradproc(theta,ds);
    local y,one,x,z,be,h,xb,zh,zh1,e,per1,gr1,gr2,grad;
    y=(ds[.,1]+.01)*100/10002;
    one=ones(rows(ds),1);
if ind==0;
    x=one;
    else;
    x=one~ds[.,2:rows(ind)+1];
endif;
if indV==0;
    z=one;	     
    else;
    z=one~ds[.,cols(ds)-rows(indV)+1:cols(ds)];
endif;		     
    be=theta[1:cols(x),1];
    h=trimr(theta,rows(be),0);      
    xb=exp(x*be);
    zh=exp(z*h);
    zh1=zh+1;
    e=xb./(1+xb);
    per1=(-x.*e+x.*(e^2)).*zh1;

    gr1=psi(e.*zh1+(1-e).*zh1-1).*(x.*e.*zh1-(e^2).*zh1.*x+per1)-
        psi(e.*zh1-e).*(x.*e.*zh1-(e^2).*zh1.*x-x.*e+(e^2).*x)-
        psi((1-e).*zh1-1+e).*(per1+x.*e-(e^2).*x)+
        (x.*e.*zh1-(e^2).*zh1.*x-x.*e+(e^2).*x).*ln(y)+
        (per1+x.*e-(e^2).*x).*ln(1-y);
    gr2=psi(e.*zh1+(1-e).*zh1-1).*(e.*z.*zh+(1-e).*z.*zh)-
        (psi(e.*zh1-e).*xb.*z.*zh)./(1+xb)-
        psi((1-e).*zh1-1+e).*(1-e).*z.*zh+xb.*z.*zh.*ln(y)./(1+xb)+
        (1-e).*z.*zh.*ln(1-y);
    grad=gr1~gr2;
    retp(grad);endp;

proc loglik(theta,ds);
    local y,one,x,z,be,h,xb,zh,e,v,a,b,llik,ds1;
		     
    y=(ds[.,1]+.01)*100/10002;
    one=ones(rows(ds),1);
if ind==0;
    x=one;
    else;
    x=one~ds[.,2:rows(ind)+1];
endif;
if indV==0;
    z=one;	     
    else;
    z=one~ds[.,cols(ds)-rows(indV)+1:cols(ds)];
endif;		     
    be=theta[1:cols(x),1];
    h=trimr(theta,rows(be),0);      
    xb=exp(x*be);
    zh=exp(z*h);
    e=xb./(1+xb);
    v=e.*(1-e).*(1/(zh+1));
    a=((e^2).*(1-e))./v-e;
    b=(e.*(1-e)^2)./v-(1-e);
    llik=lng(a+b)-lng(a)-lng(b)+(a-1).*ln(y)+(b-1).*ln(1-y);
    retp(llik);endp;

    if ind==0;
      _cml_ParNames="const"|"const";
    elseif indV==0;
      _cml_ParNames="const"|ind|"const";
    else;
      _cml_ParNames="const"|ind|"const"|indV;
    endif;

/* _cml_GradCheck=1;
_cml_GradProc=&gradproc;  */
_cml_Options = { none }; 
_cml_DirTol=0.00001; 

t=dta $+ dep $+ ".dir.out"; 
output file=^t on; 
    print "dependent variable=" ;; $dep; 
    {b,logl,g,vc,ret}=CMLprt(CML(dataset,0,&loglik,stval));
@ cond(_cml_FinalHess); @

/* set ind and indV matrices */
y=(dataset[.,1]+.01)*100/10002;
one=ones(rows(dataset),1);

if ind==0;
  x=one;
  else;
  x=ones(rows(dataset),1)~dataset[.,2:rows(ind)+1]; 
endif;

if indV==0;
  z=one;
  else;
  z=ones(rows(dataset),1)~dataset[.,cols(dataset)-rows(indV)+1:cols(dataset)]; 
endif;		     

/* get predicted values of y */
    bb=trimr(b,0,1);
    if indV/=0;
       bb=trimr(b,0,rows(indV)+1);
    endif;
    xb=exp(x*bb);
    eyb=xb./(1+xb);

/* set descriptives for x and z */
meanx=meanc(x);  @ these are k1X1 vectors @
stdx=stdc(x);	
minx=minc(x);	
maxx=maxc(x);	

meanz=meanc(z);

/* create switching parameter */

if ind/=0;
sw=zeros(1,cols(x)-1)|eye(cols(x)-1);
xl=meanx-stdx.*sw;           @ these are kXk-1 vectors @
xh=meanx+stdx.*sw;       
xmin=meanx.*(1-sw)+minx.*sw;  
xmax=meanx.*(1-sw)+maxx.*sw;
endif;

/* generate the parameter vectors */
    be=b[1:cols(x),.];      @ chop off parms for alpha (k1X1) @
    h=trimr(b,rows(be),0);  @ chop off parms for beta (k2X1) @

/* get predicted means */

    em=(exp(meanx'*be)./(1+exp(meanx'*be)))'; @ these are nX1 vectors @

    if ind/=0;
      emin=(exp(xmin'*be)./(1+exp(xmin'*be)))';
      emax=(exp(xmax'*be)./(1+exp(xmax'*be)))';
      el=(exp(xl'*be)./(1+exp(xl'*be)))';
      eh=(exp(xh'*be)./(1+exp(xh'*be)))';
    endif;
  
/* get first differences for the mean */
    if ind/=0;
    fdm2=eh-el;
    fdmm=emax-emin;
    endif;
    
/* get predicted variances for variables affecting the mean */

  betasim=rndmn(b,vc,1000);
  bs=betasim[.,1:cols(x)];
  hs=betasim[.,cols(x)+1:cols(betasim)];

  ml=(exp(bs*xl)./(1+exp(bs*xl)));
  mh=(exp(bs*xh)./(1+exp(bs*xh)));
  m0=(exp(bs*xmin)./(1+exp(bs*xmin)));
  m1=(exp(bs*xmax)./(1+exp(bs*xmax)));
  
@  if indv/=0; @
    j=1; i=1; hx=zeros(1000,rows(c)); 
    do until j>rows(c);
       if c[j]==1;
	 hx[.,j]=hx[.,j]+hs[.,i];
	 i=i+1;
       endif;
    j=j+1;
    endo;
@  endif; @

    dm=(1/(exp(meanz'*h)+1));
    vm=em.*(1-em).*dm;

@  if indV/=0; @
      dmin=(1/(exp(hx*xmin)+1));
      dmax=(1/(exp(hx*xmax)+1));
      dl=(1/(exp(hx*xl)+1));
      dh=(1/(exp(hx*xh)+1));
      vmin=m0.*(1-m0).*dmin;
      vmax=m1.*(1-m1).*dmax;
      vl=ml.*(1-ml).*dl;
      vh=mh.*(1-mh).*dh;

      fdv2=vh-vl;
      fdvm=vmax-vmin;
@  endif; @

  if ind/=0;
    print $ind;; meanc(fdm2)~meanc(fdmm);
  endif;
  
@  if indV/=0; @
    print $ind;; meanc(fdv2)~stdc(fdv2)~meanc(fdvm)~stdc(fdvm);
@  endif; @
    
format /rd 8,5;

print "alpha=";; ((em^2).*(1-em))./vm-em;
print "beta=";; (em.*(1-em)^2)./vm-(1-em);
alp=((em^2).*(1-em))./vm-em;
bet=(em.*(1-em)^2)./vm-(1-em);
print "ave mean=";; alp/(alp+bet);
print "ave var=";; alp*bet/((alp+bet)^2*(alp+bet+1)); 

/* run ols */

{ vnam,m,bols,stb,vcols,stderr,sigma,cx,rsq,resid,dbw } = ols(0,y,x);

/* generate first differences for ols */
  olsl=xl'*bols;
  olsh=xh'*bols;
  
  olsh-olsl;

/* run ols with logit transformation*/

yt=ln(y./(1-y));

{ vnam,m,bolsl,stbl,vcols,stderrl,sigma,cx,rsq,resid,dbw } = ols(0,yt,x);

/* generate first differences for ols */
  olsl=(exp(xl'*bolsl))./(1+exp(xl'*bolsl));
  olsh=(exp(xh'*bolsl))./(1+exp(xh'*bolsl)); 
  
  olsh-olsl;

  ely=(exp(x*bolsl))./(1+exp(x*bolsl));
  
let pe=perinst;
if rows(y)==50 and stof(dep)/=stof(pe);
/* run ols for logged model */
  
let depl=lpemp;
let indl=ltask lwealth rights lelite lcol;
varsl=depl|indl;
dataset2=listw(dta,varsl,sel);
ly=(dataset2[.,1]);
lx=ones(rows(ly),1)~(dataset2[.,2:cols(dataset2)]);

{ lvnam,lm,lbols,lstb,lvcols,lstderr,lsigma,lcx,lrsq,lresid,ldbw } = ols(0,ly,lx);


/* set descriptives for x and z */
meanlx=meanc(lx);  @ these are k1X1 vectors @
stdlx=stdc(lx);	
minlx=minc(lx);	
maxlx=maxc(lx);	

/* create switching parameter */

if ind/=0;
lsw=zeros(1,cols(lx)-1)|eye(cols(lx)-1);
lxl=meanlx-stdlx.*lsw;           @ these are kXk-1 vectors @
lxh=meanlx+stdlx.*lsw;       
lxmin=meanlx.*(1-lsw)+minlx.*lsw;  
lxmax=meanlx.*(1-lsw)+maxlx.*lsw;
endif;

/* generate first differences for logged ols */

  lolsl=(exp(lxl'*lbols)-1)*100/10101;
  lolsh=(exp(lxh'*lbols)-1)*100/10101;
  
  lolsh-lolsl; 

/* get predicted data */
predly=lx*lbols;
predyl=(exp(predly)-1)*100/10101;
yadj=(exp(ly)-1)*100/10101;
minc(predyl)~maxc(predyl);
minc(yadj)~maxc(yadj);
msel=sumc((yadj-predyl)^2)/rows(y); 
endif;

/* compare mse of y */
mseb=sumc((y-eyb)^2)/rows(y);
mseo=sumc((y-x*bols)^2)/rows(y);
mset=sumc((y-ely)^2)/rows(y);

print "extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS";
minc(y)~maxc(y);
minc(eyb)~maxc(eyb);
minc(x*bols)~maxc(x*bols);
minc(ely)~maxc(ely);
if rows(y)==50 and stof(dep)/=stof(pe);
minc(predyl)~maxc(predyl);
endif;
print " percentage of OLS and lnOLS falling outside of [0,1]";
sumc(x*bols.>1)/rows(y);
sumc(x*bols.<0)/rows(y);
sumc(ely.>1)/rows(y);
sumc(ely.<0)/rows(y);
if rows(y)==50 and stof(dep)/=stof(pe);
sumc(predyl.>1)/rows(y);
sumc(predyl.<0)/rows(y); 
endif;

rbro=mseb/mseo;
print "Beta is better if rb/ro<1";;rbro;
print "beta mse=";;mseb;
print "ols mse=";;mseo;
rbrt=mseb/mset;
print "Beta is better than logit trans if rb/ro<1";;rbrt;
if rows(y)==50 and stof(dep)/=stof(pe);
rbrl=mseb/msel; 
print "Beta is better if rb/rl<1";;rbrl; 
endif;

y~eyb~(x*bols)~ely;
output off;


dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/20/01   9:43 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         3.94237
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const           -6.6721        1.3844   -4.819   0.0000      0.0000
TASK             0.1032        0.0632    1.632   0.0513      0.0000
RIGHTS           0.1772        0.1371    1.293   0.0980      0.0000
ELITE            4.9268        1.2856    3.832   0.0001      0.0000
SAL             -0.1794        0.1772   -1.013   0.1556      0.0000
COL              0.1338        0.0778    1.719   0.0428      0.0000
WI               3.3324        1.1787    2.827   0.0023      0.0000
LA               1.6236        1.2543    1.294   0.0978      0.0000
DE              -1.2645        1.1161   -1.133   0.1286      0.0000
RI              -3.0457        1.2172   -2.502   0.0062      0.0000
const            0.1049        0.2469    0.425   0.3355      0.0000

Correlation matrix of the parameters
   1.000   0.303  -0.028  -0.549   0.235  -0.813  -0.209  -0.169   0.085
   0.160  -0.474
   0.303   1.000  -0.103  -0.270   0.048  -0.452   0.130  -0.020   0.055
   0.026   0.325
  -0.028  -0.103   1.000  -0.110  -0.318  -0.010  -0.155   0.086  -0.058
  -0.145   0.172
  -0.549  -0.270  -0.110   1.000   0.163   0.058   0.124   0.135  -0.068
  -0.363   0.364
   0.235   0.048  -0.318   0.163   1.000  -0.403   0.004   0.023  -0.056
  -0.056  -0.119
  -0.813  -0.452  -0.010   0.058  -0.403   1.000   0.102   0.070  -0.064
   0.060   0.122
  -0.209   0.130  -0.155   0.124   0.004   0.102   1.000   0.041   0.001
  -0.021   0.284
  -0.169  -0.020   0.086   0.135   0.023   0.070   0.041   1.000  -0.009
  -0.053   0.113
   0.085   0.055  -0.058  -0.068  -0.056  -0.064   0.001  -0.009   1.000
   0.060  -0.095
   0.160   0.026  -0.145  -0.363  -0.056   0.060  -0.021  -0.053   0.060
   1.000  -0.251
  -0.474   0.325   0.172   0.364  -0.119   0.122   0.284   0.113  -0.095
  -0.251   1.000

Number of iterations    3
Minutes to convergence     0.00499

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
      0.19153487       0.59031130 
      0.10335904       0.14316332 
      0.32717045       0.60853242 
    -0.074755224      -0.15674071 
      0.15365781       0.33164757 
      0.18222978       0.65227853 
     0.089219543       0.38018681 
    -0.069524348      -0.17515386 
     -0.16672916      -0.25871816 

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
     0.037163861      0.020409767     0.0026316821      0.027488134 
     0.021724941      0.016114706      0.025682816      0.018272513 
     0.059445348      0.012467185      0.069951098      0.012246044 
    -0.015948474      0.015157753     -0.039018115      0.032954106 
     0.031328478      0.017368367      0.050328230      0.023589302 
     0.036875906      0.012418790     -0.040217688      0.033734337 
     0.018139710      0.014187421    -0.0033633477      0.029758540 
    -0.014167499      0.013026564     -0.043489347      0.033579063 
    -0.034238010      0.012553080     -0.080203125      0.021248782 
alpha= 0.29381 
beta= 0.81677 
ave mean= 0.26456 
ave var= 0.09219 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.486      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.983      Std error of est:                 0.223
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.982863    0.232135   -4.234020     0.000       ---         ---  
X1           0.014357    0.009538    1.505231     0.140    0.189569    0.606581
X2           0.021072    0.027309    0.771619     0.445    0.086966    0.441778
X3           0.975895    0.242002    4.032584     0.000    0.467892    0.621866
X4          -0.045143    0.037059   -1.218141     0.230   -0.132979    0.008212
X5           0.034592    0.014806    2.336321     0.025    0.281867    0.453771
X6           0.829871    0.230644    3.598056     0.001    0.322567    0.313797
X7           0.168207    0.228687    0.735535     0.466    0.065381   -0.035959
X8          -0.217876    0.227179   -0.959052     0.343   -0.084688   -0.082752
X9          -0.535798    0.240679   -2.226191     0.032   -0.208262   -0.082752

 0.13794 
 0.06328 
 0.34047 
-0.09676 
 0.20511 
 0.23472 
 0.04758 
-0.06162 
-0.15155 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                 2177.498      Degrees of freedom:                  40
R-squared:                   0.763      Rbar-squared:                     0.710
Residual SS:               515.180      Std error of est:                 3.589
F(9,40):                    14.341      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -27.065860    3.741677   -7.233618     0.000       ---         ---  
X1           0.182558    0.153736    1.187478     0.242    0.131565    0.610722
X2           0.674086    0.440184    1.531372     0.134    0.151837    0.485433
X3          20.649065    3.900732    5.293639     0.000    0.540340    0.659039
X4          -0.688691    0.597333   -1.152944     0.256   -0.110724    0.025887
X5           0.610057    0.238653    2.556254     0.014    0.271311    0.459219
X6          13.313469    3.717654    3.581148     0.001    0.282439    0.285778
X7           7.393776    3.686110    2.005848     0.052    0.156856    0.042996
X8          -5.750007    3.661796   -1.570269     0.124   -0.121984   -0.112859
X9         -12.652946    3.879406   -3.261568     0.002   -0.268427   -0.112859

 0.03471 
 0.04149 
 0.40203 
-0.02830 
 0.09780 
 0.10494 
 0.04326 
-0.03170 
-0.09601 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  202.870      Degrees of freedom:                  44
R-squared:                   0.611      Rbar-squared:                     0.567
Residual SS:                78.897      Std error of est:                 1.339
F(5,44):                    13.828      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.437198    5.732646   -2.692858     0.010       ---         ---  
X1           0.914732    0.399571    2.289285     0.027    0.346257    0.704605
X2           0.853768    0.929137    0.918883     0.363    0.095548    0.335304
X3           0.190633    0.153481    1.242064     0.221    0.140680    0.510757
X4           1.874436    0.793981    2.360808     0.023    0.297192    0.611638
X5           1.734884    1.389473    1.248591     0.218    0.159794    0.509765

 0.16651 
 0.04262 
 0.06322 
 0.13992 
 0.07209 
-0.00341  2.70982 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00010  0.99990 
 0.04394  0.94777 
-0.19229  0.99990 
 0.00001  0.99993 
-0.00341  2.70982 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.28000 
 0.00000 
 0.00000 
 0.08000 
 0.06000 
Beta is better if rb/ro<1 1.13640 
beta mse= 0.04507 
ols mse= 0.03966 
Beta is better than logit trans if rb/ro<1 1.16947 
Beta is better if rb/rl<1 0.18641 

 0.00010  0.08158 -0.07961  0.00664 
 0.05209  0.38617  0.30472  0.28912 
 0.00010  0.16636  0.11106  0.06055 
 0.15407  0.51394  0.38584  0.45850 
 0.00010  0.07571 -0.02272  0.01498 
 0.00010  0.05444 -0.12698  0.00354 
 0.00010  0.09110 -0.04232  0.03373 
 0.00010  0.04394 -0.19229  0.00086 
 0.00010  0.15168  0.11555  0.03406 
 0.00010  0.09612  0.00010  0.25147 
 0.00010  0.05534 -0.11179 -0.00133 
 0.00010  0.17332  0.11532  0.08452 
 0.07808  0.13308  0.02734  0.06133 
 0.00010  0.10081 -0.01760  0.00512 
 0.99990  0.76863  0.69653  0.79554 
 0.00010  0.19049  0.13741  0.01375 
 0.00010  0.10253  0.01201  0.01324 
 0.00010  0.10260  0.00789  0.03061 
 0.01810  0.30834  0.28031  0.18157 
 0.00010  0.15729  0.11437  0.08535 
 0.00010  0.15868  0.09662  0.02095 
 0.00010  0.10766 -0.02000  0.11391 
 0.00010  0.36001  0.29239  0.22413 
 0.00010  0.11322 -0.02869  0.04000 
 0.00010  0.09039 -0.01453  0.01817 
 0.99990  0.70634  0.56318  0.66226 
 0.00010  0.10600 -0.00508  0.04083 
 0.00010  0.14744  0.08880  0.04181 
 0.00010  0.05257 -0.14172 -0.00341 
 0.00010  0.04825 -0.16405 -0.00026 
 0.00010  0.08042 -0.07384  0.01248 
 0.11808  0.30767  0.11808  0.01957 
 0.00010  0.09612  0.00010  0.53335 
 0.09208  0.27985  0.20716  0.14828 
 0.02310  0.11558  0.02300  0.06231 
 0.45501  0.43750  0.34223  0.29769 
 0.02709  0.10741  0.03187  0.03972 
 0.03909  0.18868  0.12291  0.07361 
 0.10608  0.68702  0.55748  0.67046 
 0.16907  0.38803  0.29378  0.51153 
 0.14307  0.46879  0.35975  0.24517 
 0.99990  0.55875  0.40156  0.53407 
 0.17706  0.38192  0.26689  0.24583 
 0.35103  0.70006  0.60841  0.48117 
 0.99990  0.79118  0.60256  1.02579 
 0.43201  0.94712  0.83215  2.46962 
 0.99990  0.90382  0.99990  0.14334 
 0.99990  0.86109  0.73604  1.87315 
 0.99990  0.94777  0.91111  2.70982 
 0.99990  0.81275  0.71373  0.95607 
dependent variable=             PVT 

===============================================================================
                     ** A Beta Model, Numerical Solution **                    
===============================================================================
 CML Version 1.0.0                                           6/20/01   9:44 pm
===============================================================================

return code =    0
normal convergence

Mean log-likelihood         4.19854
Number of cases     50

Covariance of the parameters computed by the following method:
Inverse of computed Hessian

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient
------------------------------------------------------------------
const          -11.1562        1.3912   -8.019   0.0000      0.0000
TASK             0.2092        0.0583    3.586   0.0002      0.0000
RIGHTS           0.4642        0.1389    3.342   0.0004      0.0000
ELITE           10.7173        1.3786    7.774   0.0000      0.0000
SAL             -0.0464        0.1436   -0.323   0.3734      0.0000
COL              0.0291        0.0724    0.402   0.3439      0.0000
WI               6.0618        1.1459    5.290   0.0000      0.0000
LA               3.6721        0.5949    6.173   0.0000      0.0000
DE              -1.0571        1.0366   -1.020   0.1539      0.0000
RI              -2.2694        1.4355   -1.581   0.0570      0.0000
const            8.2307        1.1334    7.262   0.0000      0.0000
RIGHTS          -0.3860        0.1397   -2.763   0.0029      0.0000
ELITE           -9.7710        1.5709   -6.220   0.0000      0.0000

Correlation matrix of the parameters
   1.000   0.181  -0.148  -0.637   0.226  -0.703  -0.206  -0.562   0.077
   0.100  -0.412   0.373   0.233
   0.181   1.000   0.065  -0.133   0.035  -0.466   0.190   0.169   0.038
   0.018   0.246   0.025  -0.159
  -0.148   0.065   1.000   0.006  -0.304  -0.026  -0.119   0.347  -0.066
  -0.117   0.215  -0.299  -0.083
  -0.637  -0.133   0.006   1.000   0.148   0.021   0.204   0.501  -0.062
  -0.206   0.555  -0.100  -0.497
   0.226   0.035  -0.304   0.148   1.000  -0.429   0.064   0.044  -0.022
  -0.002   0.094   0.137  -0.169
  -0.703  -0.466  -0.026   0.021  -0.429   1.000  -0.008   0.076  -0.065
   0.011  -0.173  -0.262   0.274
  -0.206   0.190  -0.119   0.204   0.064  -0.008   1.000   0.225   0.006
   0.021   0.311   0.038  -0.273
  -0.562   0.169   0.347   0.501   0.044   0.076   0.225   1.000  -0.021
  -0.058   0.596  -0.313  -0.444
   0.077   0.038  -0.066  -0.062  -0.022  -0.065   0.006  -0.021   1.000
   0.062   0.014  -0.035  -0.033
   0.100   0.018  -0.117  -0.206  -0.002   0.011   0.021  -0.058   0.062
   1.000   0.043  -0.041  -0.075
  -0.412   0.246   0.215   0.555   0.094  -0.173   0.311   0.596   0.014
   0.043   1.000  -0.242  -0.932
   0.373   0.025  -0.299  -0.100   0.137  -0.262   0.038  -0.313  -0.035
  -0.041  -0.242   1.000  -0.038
   0.233  -0.159  -0.083  -0.497  -0.169   0.274  -0.273  -0.444  -0.033
  -0.075  -0.932  -0.038   1.000

Number of iterations    5
Minutes to convergence     0.02200

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
      0.13028889       0.83648469 
     0.085972119       0.14443366 
      0.29181084       0.74414670 
   -0.0058272479     -0.013669874 
     0.010121791      0.021904966 
      0.10833443       0.90626697 
     0.062655354       0.65079159 
    -0.017571251     -0.040662659 
    -0.038050740     -0.058090213 

            TASK 
          RIGHTS 
           ELITE 
             SAL 
             COL 
              WI 
              LA 
              DE 
              RI 
     0.011893403     0.0049903225      0.011897242     0.0093290042 
     0.017245542     0.0072208357      0.034541950      0.014786017 
     0.082702895      0.018343991       0.14538530      0.031266799 
  -0.00061393967     0.0020698404   -0.00064195571     0.0048403944 
    0.0010910709     0.0030103884     0.0025059320     0.0065071845 
     0.010250851     0.0044038221   -0.00032467207     0.0057125160 
    0.0060505845     0.0021307312      0.016135080     0.0067407276 
   -0.0017920183     0.0020431308    -0.0031519392     0.0046231495 
   -0.0039647640     0.0032494093    -0.0053876502     0.0042868779 
alpha= 0.52009 
beta= 7.79596 
ave mean= 0.06254 
ave var= 0.00629 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                    6.486      Degrees of freedom:                  40
R-squared:                   0.694      Rbar-squared:                     0.626
Residual SS:                 1.983      Std error of est:                 0.223
F(9,40):                    10.094      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT    -0.982863    0.232135   -4.234020     0.000       ---         ---  
X1           0.014357    0.009538    1.505231     0.140    0.189569    0.606581
X2           0.021072    0.027309    0.771619     0.445    0.086966    0.441778
X3           0.975895    0.242002    4.032584     0.000    0.467892    0.621866
X4          -0.045143    0.037059   -1.218141     0.230   -0.132979    0.008212
X5           0.034592    0.014806    2.336321     0.025    0.281867    0.453771
X6           0.829871    0.230644    3.598056     0.001    0.322567    0.313797
X7           0.168207    0.228687    0.735535     0.466    0.065381   -0.035959
X8          -0.217876    0.227179   -0.959052     0.343   -0.084688   -0.082752
X9          -0.535798    0.240679   -2.226191     0.032   -0.208262   -0.082752

 0.13794 
 0.06328 
 0.34047 
-0.09676 
 0.20511 
 0.23472 
 0.04758 
-0.06162 
-0.15155 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                 2177.498      Degrees of freedom:                  40
R-squared:                   0.763      Rbar-squared:                     0.710
Residual SS:               515.180      Std error of est:                 3.589
F(9,40):                    14.341      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -27.065860    3.741677   -7.233618     0.000       ---         ---  
X1           0.182558    0.153736    1.187478     0.242    0.131565    0.610722
X2           0.674086    0.440184    1.531372     0.134    0.151837    0.485433
X3          20.649065    3.900732    5.293639     0.000    0.540340    0.659039
X4          -0.688691    0.597333   -1.152944     0.256   -0.110724    0.025887
X5           0.610057    0.238653    2.556254     0.014    0.271311    0.459219
X6          13.313469    3.717654    3.581148     0.001    0.282439    0.285778
X7           7.393776    3.686110    2.005848     0.052    0.156856    0.042996
X8          -5.750007    3.661796   -1.570269     0.124   -0.121984   -0.112859
X9         -12.652946    3.879406   -3.261568     0.002   -0.268427   -0.112859

 0.03471 
 0.04149 
 0.40203 
-0.02830 
 0.09780 
 0.10494 
 0.04326 
-0.03170 
-0.09601 
Valid cases:                    50      Dependent variable:                   Y
Missing cases:                   0      Deletion method:                   None
Total SS:                  202.870      Degrees of freedom:                  44
R-squared:                   0.611      Rbar-squared:                     0.567
Residual SS:                78.897      Std error of est:                 1.339
F(5,44):                    13.828      Probability of F:                 0.000

                         Standard                 Prob   Standardized  Cor with
Variable     Estimate      Error      t-value     >|t|     Estimate    Dep Var
-------------------------------------------------------------------------------
CONSTANT   -15.437198    5.732646   -2.692858     0.010       ---         ---  
X1           0.914732    0.399571    2.289285     0.027    0.346257    0.704605
X2           0.853768    0.929137    0.918883     0.363    0.095548    0.335304
X3           0.190633    0.153481    1.242064     0.221    0.140680    0.510757
X4           1.874436    0.793981    2.360808     0.023    0.297192    0.611638
X5           1.734884    1.389473    1.248591     0.218    0.159794    0.509765

 0.16651 
 0.04262 
 0.06322 
 0.13992 
 0.07209 
-0.00341  2.70982 
 0.00000  0.99000 
extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS
 0.00010  0.99990 
 0.00069  0.99292 
-0.19229  0.99990 
 0.00001  0.99993 
-0.00341  2.70982 
 percentage of OLS and lnOLS falling outside of [0,1]
 0.00000 
 0.28000 
 0.00000 
 0.00000 
 0.08000 
 0.06000 
Beta is better if rb/ro<1 0.75284 
beta mse= 0.02986 
ols mse= 0.03966 
Beta is better than logit trans if rb/ro<1 0.77475 
Beta is better if rb/rl<1 0.12349 

 0.00010  0.00391 -0.07961  0.00664 
 0.05209  0.23933  0.30472  0.28912 
 0.00010  0.01111  0.11106  0.06055 
 0.15407  0.43777  0.38584  0.45850 
 0.00010  0.00120 -0.02272  0.01498 
 0.00010  0.00169 -0.12698  0.00354 
 0.00010  0.00731 -0.04232  0.03373 
 0.00010  0.00188 -0.19229  0.00086 
 0.00010  0.00727  0.11555  0.03406 
 0.00010  0.02188  0.00010  0.25147 
 0.00010  0.00069 -0.11179 -0.00133 
 0.00010  0.02242  0.11532  0.08452 
 0.07808  0.01598  0.02734  0.06133 
 0.00010  0.01561 -0.01760  0.00512 
 0.99990  0.63196  0.69653  0.79554 
 0.00010  0.04466  0.13741  0.01375 
 0.00010  0.00634  0.01201  0.01324 
 0.00010  0.00216  0.00789  0.03061 
 0.01810  0.03177  0.28031  0.18157 
 0.00010  0.00715  0.11437  0.08535 
 0.00010  0.02645  0.09662  0.02095 
 0.00010  0.00807 -0.02000  0.11391 
 0.00010  0.12152  0.29239  0.22413 
 0.00010  0.01569 -0.02869  0.04000 
 0.00010  0.00388 -0.01453  0.01817 
 0.99990  0.64973  0.56318  0.66226 
 0.00010  0.00855 -0.00508  0.04083 
 0.00010  0.01126  0.08880  0.04181 
 0.00010  0.00240 -0.14172 -0.00341 
 0.00010  0.00191 -0.16405 -0.00026 
 0.00010  0.00939 -0.07384  0.01248 
 0.11808  0.12398  0.11808  0.01957 
 0.00010  0.33079  0.00010  0.53335 
 0.09208  0.11981  0.20716  0.14828 
 0.02310  0.00772  0.02300  0.06231 
 0.45501  0.22763  0.34223  0.29769 
 0.02709  0.00366  0.03187  0.03972 
 0.03909  0.03527  0.12291  0.07361 
 0.10608  0.62422  0.55748  0.67046 
 0.16907  0.13241  0.29378  0.51153 
 0.14307  0.37898  0.35975  0.24517 
 0.99990  0.55306  0.40156  0.53407 
 0.17706  0.28483  0.26689  0.24583 
 0.35103  0.44417  0.60841  0.48117 
 0.99990  0.82045  0.60256  1.02579 
 0.43201  0.99292  0.83215  2.46962 
 0.99990  0.97217  0.99990  0.14334 
 0.99990  0.91414  0.73604  1.87315 
 0.99990  0.99055  0.91111  2.70982 
 0.99990  0.81954  0.71373  0.95607 

code used to generate the above results:

library cml;
#include cml.ext;
CMLset;

__title=" ** A Beta Model, Numerical Solution **";
dta="/home/gov/faculty/ppaolino/parr/gaydata1";
let dep=pvt;
let ind=task rights elite sal col wi la de ri;
let indV=rights elite;
let sel=0;

c={1,0,1,1,0,0,0,0,0,0};

if ind==0;
   vars=dep;
   elseif indV==0; 
   vars=dep|ind;    
   else;
   vars=dep|ind|indV;
endif;

dataset=listw(dta,vars,sel);

stval=   -11.1562 |
	   0.2092 |
	   0.4642 |
	  10.7173 |
	  -0.0464 |
	   0.0291 |
	   6.0618 |
	   3.6721 |
	  -1.0571 |
	  -2.2694 |
	   8.2307 |
	  -0.3860 |
	  -9.7710 ;

	 
proc psi(x);
  local p;
  x=x+6;
  p=1/(x.*x);
  p=(((0.004166666666667*p-0.003968253986254).*p+
      0.008333333333333).*p-0.083333333333333).*p;
  p=p+ln(x)-0.5/x-1/(x-1)-1/(x-2)-1/(x-3)-1/(x-4)-1/(x-5)-1/(x-6);
retp(p);
endp;

proc gradproc(theta,ds);
    local y,one,x,z,be,h,xb,zh,zh1,e,per1,gr1,gr2,grad;
    y=(ds[.,1]+.01)*100/10002;
    one=ones(rows(ds),1);
if ind==0;
    x=one;
    else;
    x=one~ds[.,2:rows(ind)+1];
endif;
if indV==0;
    z=one;	     
    else;
    z=one~ds[.,cols(ds)-rows(indV)+1:cols(ds)];
endif;		     
    be=theta[1:cols(x),1];
    h=trimr(theta,rows(be),0);      
    xb=exp(x*be);
    zh=exp(z*h);
    zh1=zh+1;
    e=xb./(1+xb);
    per1=(-x.*e+x.*(e^2)).*zh1;

    gr1=psi(e.*zh1+(1-e).*zh1-1).*(x.*e.*zh1-(e^2).*zh1.*x+per1)-
        psi(e.*zh1-e).*(x.*e.*zh1-(e^2).*zh1.*x-x.*e+(e^2).*x)-
        psi((1-e).*zh1-1+e).*(per1+x.*e-(e^2).*x)+
        (x.*e.*zh1-(e^2).*zh1.*x-x.*e+(e^2).*x).*ln(y)+
        (per1+x.*e-(e^2).*x).*ln(1-y);
    gr2=psi(e.*zh1+(1-e).*zh1-1).*(e.*z.*zh+(1-e).*z.*zh)-
        (psi(e.*zh1-e).*xb.*z.*zh)./(1+xb)-
        psi((1-e).*zh1-1+e).*(1-e).*z.*zh+xb.*z.*zh.*ln(y)./(1+xb)+
        (1-e).*z.*zh.*ln(1-y);
    grad=gr1~gr2;
    retp(grad);endp;

proc loglik(theta,ds);
    local y,one,x,z,be,h,xb,zh,e,v,a,b,llik,ds1;
		     
    y=(ds[.,1]+.01)*100/10002;
    one=ones(rows(ds),1);
if ind==0;
    x=one;
    else;
    x=one~ds[.,2:rows(ind)+1];
endif;
if indV==0;
    z=one;	     
    else;
    z=one~ds[.,cols(ds)-rows(indV)+1:cols(ds)];
endif;		     
    be=theta[1:cols(x),1];
    h=trimr(theta,rows(be),0);      
    xb=exp(x*be);
    zh=exp(z*h);
    e=xb./(1+xb);
    v=e.*(1-e).*(1/(zh+1));
    a=((e^2).*(1-e))./v-e;
    b=(e.*(1-e)^2)./v-(1-e);
    llik=lng(a+b)-lng(a)-lng(b)+(a-1).*ln(y)+(b-1).*ln(1-y);
    retp(llik);endp;

    if ind==0;
      _cml_ParNames="const"|"const";
    elseif indV==0;
      _cml_ParNames="const"|ind|"const";
    else;
      _cml_ParNames="const"|ind|"const"|indV;
    endif;

/* _cml_GradCheck=1;
_cml_GradProc=&gradproc;  */
_cml_Options = { none }; 
_cml_DirTol=0.00001; 

t=dta $+ dep $+ ".dir.out"; 
output file=^t on; 
    print "dependent variable=" ;; $dep; 
    {b,logl,g,vc,ret}=CMLprt(CML(dataset,0,&loglik,stval));
@ cond(_cml_FinalHess); @

/* set ind and indV matrices */
y=(dataset[.,1]+.01)*100/10002;
one=ones(rows(dataset),1);

if ind==0;
  x=one;
  else;
  x=ones(rows(dataset),1)~dataset[.,2:rows(ind)+1]; 
endif;

if indV==0;
  z=one;
  else;
  z=ones(rows(dataset),1)~dataset[.,cols(dataset)-rows(indV)+1:cols(dataset)]; 
endif;		     

/* get predicted values of y */
    bb=trimr(b,0,1);
    if indV/=0;
       bb=trimr(b,0,rows(indV)+1);
    endif;
    xb=exp(x*bb);
    eyb=xb./(1+xb);

/* set descriptives for x and z */
meanx=meanc(x);  @ these are k1X1 vectors @
stdx=stdc(x);	
minx=minc(x);	
maxx=maxc(x);	

meanz=meanc(z);

/* create switching parameter */

if ind/=0;
sw=zeros(1,cols(x)-1)|eye(cols(x)-1);
xl=meanx-stdx.*sw;           @ these are kXk-1 vectors @
xh=meanx+stdx.*sw;       
xmin=meanx.*(1-sw)+minx.*sw;  
xmax=meanx.*(1-sw)+maxx.*sw;
endif;

/* generate the parameter vectors */
    be=b[1:cols(x),.];      @ chop off parms for alpha (k1X1) @
    h=trimr(b,rows(be),0);  @ chop off parms for beta (k2X1) @

/* get predicted means */

    em=(exp(meanx'*be)./(1+exp(meanx'*be)))'; @ these are nX1 vectors @

    if ind/=0;
      emin=(exp(xmin'*be)./(1+exp(xmin'*be)))';
      emax=(exp(xmax'*be)./(1+exp(xmax'*be)))';
      el=(exp(xl'*be)./(1+exp(xl'*be)))';
      eh=(exp(xh'*be)./(1+exp(xh'*be)))';
    endif;
  
/* get first differences for the mean */
    if ind/=0;
    fdm2=eh-el;
    fdmm=emax-emin;
    endif;
    
/* get predicted variances for variables affecting the mean */

  betasim=rndmn(b,vc,1000);
  bs=betasim[.,1:cols(x)];
  hs=betasim[.,cols(x)+1:cols(betasim)];

  ml=(exp(bs*xl)./(1+exp(bs*xl)));
  mh=(exp(bs*xh)./(1+exp(bs*xh)));
  m0=(exp(bs*xmin)./(1+exp(bs*xmin)));
  m1=(exp(bs*xmax)./(1+exp(bs*xmax)));
  
@  if indv/=0; @
    j=1; i=1; hx=zeros(1000,rows(c)); 
    do until j>rows(c);
       if c[j]==1;
	 hx[.,j]=hx[.,j]+hs[.,i];
	 i=i+1;
       endif;
    j=j+1;
    endo;
@  endif; @

    dm=(1/(exp(meanz'*h)+1));
    vm=em.*(1-em).*dm;

@  if indV/=0; @
      dmin=(1/(exp(hx*xmin)+1));
      dmax=(1/(exp(hx*xmax)+1));
      dl=(1/(exp(hx*xl)+1));
      dh=(1/(exp(hx*xh)+1));
      vmin=m0.*(1-m0).*dmin;
      vmax=m1.*(1-m1).*dmax;
      vl=ml.*(1-ml).*dl;
      vh=mh.*(1-mh).*dh;

      fdv2=vh-vl;
      fdvm=vmax-vmin;
@  endif; @

  if ind/=0;
    print $ind;; meanc(fdm2)~meanc(fdmm);
  endif;
  
@  if indV/=0; @
    print $ind;; meanc(fdv2)~stdc(fdv2)~meanc(fdvm)~stdc(fdvm);
@  endif; @
    
format /rd 8,5;

print "alpha=";; ((em^2).*(1-em))./vm-em;
print "beta=";; (em.*(1-em)^2)./vm-(1-em);
alp=((em^2).*(1-em))./vm-em;
bet=(em.*(1-em)^2)./vm-(1-em);
print "ave mean=";; alp/(alp+bet);
print "ave var=";; alp*bet/((alp+bet)^2*(alp+bet+1)); 

/* run ols */

{ vnam,m,bols,stb,vcols,stderr,sigma,cx,rsq,resid,dbw } = ols(0,y,x);

/* generate first differences for ols */
  olsl=xl'*bols;
  olsh=xh'*bols;
  
  olsh-olsl;

/* run ols with logit transformation*/

yt=ln(y./(1-y));

{ vnam,m,bolsl,stbl,vcols,stderrl,sigma,cx,rsq,resid,dbw } = ols(0,yt,x);

/* generate first differences for ols */
  olsl=(exp(xl'*bolsl))./(1+exp(xl'*bolsl));
  olsh=(exp(xh'*bolsl))./(1+exp(xh'*bolsl)); 
  
  olsh-olsl;

  ely=(exp(x*bolsl))./(1+exp(x*bolsl));
  
let pe=perinst;
if rows(y)==50 and stof(dep)/=stof(pe);
/* run ols for logged model */
  
let depl=lpemp;
let indl=ltask lwealth rights lelite lcol;
varsl=depl|indl;
dataset2=listw(dta,varsl,sel);
ly=(dataset2[.,1]);
lx=ones(rows(ly),1)~(dataset2[.,2:cols(dataset2)]);

{ lvnam,lm,lbols,lstb,lvcols,lstderr,lsigma,lcx,lrsq,lresid,ldbw } = ols(0,ly,lx);


/* set descriptives for x and z */
meanlx=meanc(lx);  @ these are k1X1 vectors @
stdlx=stdc(lx);	
minlx=minc(lx);	
maxlx=maxc(lx);	

/* create switching parameter */

if ind/=0;
lsw=zeros(1,cols(lx)-1)|eye(cols(lx)-1);
lxl=meanlx-stdlx.*lsw;           @ these are kXk-1 vectors @
lxh=meanlx+stdlx.*lsw;       
lxmin=meanlx.*(1-lsw)+minlx.*lsw;  
lxmax=meanlx.*(1-lsw)+maxlx.*lsw;
endif;

/* generate first differences for logged ols */

  lolsl=(exp(lxl'*lbols)-1)*100/10101;
  lolsh=(exp(lxh'*lbols)-1)*100/10101;
  
  lolsh-lolsl; 

/* get predicted data */
predly=lx*lbols;
predyl=(exp(predly)-1)*100/10101;
yadj=(exp(ly)-1)*100/10101;
minc(predyl)~maxc(predyl);
minc(yadj)~maxc(yadj);
msel=sumc((yadj-predyl)^2)/rows(y); 
endif;

/* compare mse of y */
mseb=sumc((y-eyb)^2)/rows(y);
mseo=sumc((y-x*bols)^2)/rows(y);
mset=sumc((y-ely)^2)/rows(y);

print "extreme vals of y,Ey_beta,Ey_OLS,Ey_lnOLS";
minc(y)~maxc(y);
minc(eyb)~maxc(eyb);
minc(x*bols)~maxc(x*bols);
minc(ely)~maxc(ely);
if rows(y)==50 and stof(dep)/=stof(pe);
minc(predyl)~maxc(predyl);
endif;
print " percentage of OLS and lnOLS falling outside of [0,1]";
sumc(x*bols.>1)/rows(y);
sumc(x*bols.<0)/rows(y);
sumc(ely.>1)/rows(y);
sumc(ely.<0)/rows(y);
if rows(y)==50 and stof(dep)/=stof(pe);
sumc(predyl.>1)/rows(y);
sumc(predyl.<0)/rows(y); 
endif;

rbro=mseb/mseo;
print "Beta is better if rb/ro<1";;rbro;
print "beta mse=";;mseb;
print "ols mse=";;mseo;
rbrt=mseb/mset;
print "Beta is better than logit trans if rb/ro<1";;rbrt;
if rows(y)==50 and stof(dep)/=stof(pe);
rbrl=mseb/msel; 
print "Beta is better if rb/rl<1";;rbrl; 
endif;

y~eyb~(x*bols)~predyl;
output off;

